On the Efficient Generation of  <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2631903pt" id="M1" height="8.60421pt" version="1.1" viewBox="-0.0657574 -8.34102 10.6147 8.60421" width="10.6147pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><path id="g5-223" d="M563 442L553 454L479 439C463 404 440 354 416 322H414C389 422 344 454 283 454C151 454 21 310 21 162C21 48 73 -12 135 -12C182 -12 249 19 325 126H327C339 20 368 -12 407 -12C452 -12 507 21 557 110L530 136C508 107 493 92 480 92C462 92 453 123 430 253C459 292 528 386 563 442ZM318 186C290 133 235 76 202 76C175 76 154 108 154 184C154 275 198 406 247 406C288 406 313 294 318 186Z"/></g></svg>-<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2631903pt" id="M2" height="8.60421pt" version="1.1" viewBox="-0.0657574 -8.34102 9.5915 8.60421" width="9.5915pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><path id="g5-232" d="M506 405C506 432 483 454 457 454C408 454 367 413 305 342L196 211L228 373C232 393 235 410 235 418C235 442 225 454 206 454C172 454 102 416 21 346L38 316C67 337 93 353 103 353C106 353 110 342 103 311L31 -2L34 -12C73 -5 114 0 153 3L187 157C193 165 207 183 219 189L267 67C293 2 321 -12 349 -12S434 11 496 100L472 127C444 94 423 81 416 81C407 81 399 92 380 127C362 161 317 265 310 285C335 314 378 363 420 363C433 363 444 361 454 354C461 349 467 349 475 355C489 365 506 385 506 405Z"/></g></svg>-<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.445681pt" id="M3" height="12.7867pt" version="1.1" viewBox="-0.0657574 -8.34102 10.4711 12.7867" width="10.4711pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><path id="g5-234" d="M560 102L544 134C516 105 480 87 475 87C467 87 468 98 475 138C496 256 522 364 546 454H533L417 428L373 236C355 209 268 82 229 82C212 82 202 98 218 181C235 267 258 364 284 449L274 454L153 433L59 30C44 -36 21 -130 21 -169C21 -227 36 -246 61 -246C94 -246 133 -219 142 -207L139 -201C120 -182 101 -133 101 -43C101 -15 105 15 113 33H115C122 9 140 -12 159 -12C189 -12 206 -1 236 20C263 39 301 81 359 161H361C355 145 349 116 346 97C335 26 339 -12 378 -12C409 -12 473 13 560 102Z"/></g></svg><b> and </b><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2631903pt" id="M4" height="8.60421pt" version="1.1" viewBox="-0.0657574 -8.34102 10.6147 8.60421" width="10.6147pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><use xlink:href="#g5-223"/></g></svg>-<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.445681pt" id="M5" height="12.7867pt" version="1.1" viewBox="-0.0657574 -8.34102 9.5556 12.7867" width="9.5556pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><path id="g5-229" d="M504 399C504 447 482 454 463 454C435 454 404 443 367 418C321 387 273 345 216 277H214L220 304C231 354 238 388 238 411C238 443 226 454 204 454C164 454 90 418 21 352L36 320C56 343 95 363 106 363C112 363 114 354 107 324L30 -4L38 -14C66 -4 119 5 157 9L201 201C234 258 330 359 367 359C377 359 383 344 374 308L312 50C284 -66 272 -144 272 -168C272 -187 341 -246 384 -246L392 -226C389 -211 387 -181 399 -122L494 330C500 360 504 382 504 399Z"/></g></svg>-<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.445681pt" id="M6" height="12.7867pt" version="1.1" viewBox="-0.0657574 -8.34102 10.4711 12.7867" width="10.4711pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><use xlink:href="#g5-234"/></g></svg> White Samples with Applications

<div>Sample mean and confidence region (<svg height="9.06134pt" id="M606" style="vertical-align:-0.3625803pt" version="1.1" viewbox="-0.0498162 -8.69876 31.6764 9.06134" width="31.6764pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M535 290V340H323V533H265V340H52V290H265V84H323V290H535ZM535 -22V28H52V-22H535Z" id="g117-37"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,7.953,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,18.998,0)"><path d="M528 54L331 254L528 455L492 493L294 291L96 493L60 455L257 254L60 54L96 16L294 217L492 16L528 54Z" id="g117-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g></svg>sample standard deviation) of <svg height="13.2091pt" id="M607" style="vertical-align:-3.57199pt" version="1.1" viewbox="-0.0498162 -9.63711 21.4082 13.2091" width="21.4082pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,1.462,-.231)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z" id="g119-17"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="470" vert-adv-y="470"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z" id="g113-234"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="555" vert-adv-y="555"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,7.181,3.264)"><path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z" id="g190-78"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="891" vert-adv-y="891"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,15.63,3.264)"><path d="M495 163C480 117 462 85 444 65C421 39 387 34 332 34C290 34 256 36 236 47C218 57 213 77 213 131V526C213 612 222 616 301 622V650H40V622C122 616 128 611 128 526V126C128 41 120 34 36 28V0H489C498 31 519 126 525 157L495 163Z" id="g190-77"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="538" vert-adv-y="538"></glyph.data></g></svg>, for <svg height="8.91176pt" id="M608" style="vertical-align:-0.2130003pt" version="1.1" viewbox="-0.0498162 -8.69876 55.1165 8.91176" width="55.1165pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="502" vert-adv-y="502"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,10.586,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,22.324,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,28.827,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 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transform="matrix(.0135,0,0,-0.0135,48.337,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg> and <svg height="8.91176pt" id="M609" style="vertical-align:-0.2130003pt" version="1.1" viewbox="-0.0498162 -8.69876 29.0745 8.91176" width="29.0745pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M484 406C484 429 465 448 438 448C400 448 352 405 302 356L156 213L191 373C195 391 197 404 197 416C197 436 191 448 178 448C151 448 83 406 23 350L37 328C67 350 101 369 109 369C114 369 115 362 111 344L29 -5L34 -12C63 -5 86 -1 111 3C124 73 137 138 147 161C165 180 189 202 206 217C215 194 249 111 275 57C304 -1 319 -12 342 -12C368 -12 405 -5 471 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International Journal of Antennas and Propagation

fig8

Figure 8

Figure 8: On the Efficient Generation of  <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2631903pt" id="M1" height="8.60421pt" version="1.1" viewBox="-0.0657574 -8.34102 10.6147 8.60421" width="10.6147pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><path id="g5-223" d="M563 442L553 454L479 439C463 404 440 354 416 322H414C389 422 344 454 283 454C151 454 21 310 21 162C21 48 73 -12 135 -12C182 -12 249 19 325 126H327C339 20 368 -12 407 -12C452 -12 507 21 557 110L530 136C508 107 493 92 480 92C462 92 453 123 430 253C459 292 528 386 563 442ZM318 186C290 133 235 76 202 76C175 76 154 108 154 184C154 275 198 406 247 406C288 406 313 294 318 186Z"/></g></svg>-<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2631903pt" id="M2" height="8.60421pt" version="1.1" viewBox="-0.0657574 -8.34102 9.5915 8.60421" width="9.5915pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><path id="g5-232" d="M506 405C506 432 483 454 457 454C408 454 367 413 305 342L196 211L228 373C232 393 235 410 235 418C235 442 225 454 206 454C172 454 102 416 21 346L38 316C67 337 93 353 103 353C106 353 110 342 103 311L31 -2L34 -12C73 -5 114 0 153 3L187 157C193 165 207 183 219 189L267 67C293 2 321 -12 349 -12S434 11 496 100L472 127C444 94 423 81 416 81C407 81 399 92 380 127C362 161 317 265 310 285C335 314 378 363 420 363C433 363 444 361 454 354C461 349 467 349 475 355C489 365 506 385 506 405Z"/></g></svg>-<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.445681pt" id="M3" height="12.7867pt" version="1.1" viewBox="-0.0657574 -8.34102 10.4711 12.7867" width="10.4711pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><path id="g5-234" d="M560 102L544 134C516 105 480 87 475 87C467 87 468 98 475 138C496 256 522 364 546 454H533L417 428L373 236C355 209 268 82 229 82C212 82 202 98 218 181C235 267 258 364 284 449L274 454L153 433L59 30C44 -36 21 -130 21 -169C21 -227 36 -246 61 -246C94 -246 133 -219 142 -207L139 -201C120 -182 101 -133 101 -43C101 -15 105 15 113 33H115C122 9 140 -12 159 -12C189 -12 206 -1 236 20C263 39 301 81 359 161H361C355 145 349 116 346 97C335 26 339 -12 378 -12C409 -12 473 13 560 102Z"/></g></svg><b> and </b><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2631903pt" id="M4" height="8.60421pt" version="1.1" viewBox="-0.0657574 -8.34102 10.6147 8.60421" width="10.6147pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><use xlink:href="#g5-223"/></g></svg>-<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.445681pt" id="M5" height="12.7867pt" version="1.1" viewBox="-0.0657574 -8.34102 9.5556 12.7867" width="9.5556pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><path id="g5-229" d="M504 399C504 447 482 454 463 454C435 454 404 443 367 418C321 387 273 345 216 277H214L220 304C231 354 238 388 238 411C238 443 226 454 204 454C164 454 90 418 21 352L36 320C56 343 95 363 106 363C112 363 114 354 107 324L30 -4L38 -14C66 -4 119 5 157 9L201 201C234 258 330 359 367 359C377 359 383 344 374 308L312 50C284 -66 272 -144 272 -168C272 -187 341 -246 384 -246L392 -226C389 -211 387 -181 399 -122L494 330C500 360 504 382 504 399Z"/></g></svg>-<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.445681pt" id="M6" height="12.7867pt" version="1.1" viewBox="-0.0657574 -8.34102 10.4711 12.7867" width="10.4711pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><use xlink:href="#g5-234"/></g></svg> White Samples with Applications 

International Journal of Antennas and Propagation

On the Efficient Generation of -- and -- White Samples with Applications

Figure 8