Best Known (64, 64+∞, s)-Nets in Base 27
(64, 64+∞, 114)-Net over F27 — Constructive and digital
Digital (64, m, 114)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (64, 113)-sequence over F27, using
- t-expansion [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- t-expansion [i] based on digital (23, 113)-sequence over F27, using
(64, 64+∞, 325)-Net over F27 — Digital
Digital (64, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (64, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
(64, 64+∞, 1722)-Net in Base 27 — Upper bound on s
There is no (64, m, 1723)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (64, 3443, 1723)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273443, 1723, S27, 2, 3379), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4138 126508 600014 122594 701618 027975 473504 998501 519419 055119 807626 047730 696710 808920 398688 358240 206326 251585 332209 781121 791706 563912 645555 081090 822443 345931 053616 562918 146140 381386 281890 756415 154045 057993 895146 565120 844558 425541 703782 362573 203746 835660 217360 964466 906421 491926 047308 702346 287066 866333 509608 441100 104564 062897 057333 826024 557463 487769 318216 039776 352426 609053 858987 225248 088241 512598 529099 533707 081735 802890 779657 559709 488460 050060 730041 802845 129373 403487 815175 292143 724552 062660 472322 262132 150539 781399 128318 605805 622518 480099 320434 464327 147962 358350 946777 288932 951805 352719 347406 712524 313753 716707 286884 092147 218635 288715 717598 053549 187646 162091 262683 563593 346293 540457 534582 595523 395732 053769 566524 698110 909222 715226 222134 656905 053522 132053 827487 793975 139093 059193 979574 473359 926385 950849 841877 506447 971958 056032 344141 050149 437593 772237 897022 541715 105391 489017 596391 259685 214571 291426 589888 133476 865822 254202 840553 517906 219827 053687 879810 137080 739824 215007 959902 877583 007397 329900 728112 048472 911812 496279 606415 651233 331706 436065 566688 767243 518550 964501 153145 787958 672414 301376 101630 305381 834538 592412 887572 882365 283537 021388 478782 455263 949549 215341 577387 561412 403681 803863 957705 459998 188290 822324 212994 791969 573904 337511 441507 948833 723711 660695 270044 536248 647558 471472 514657 181808 627482 166854 260149 423240 742962 134145 750941 410666 711575 151842 636595 768395 576550 887807 990132 210327 893966 339037 512187 931958 768065 192486 427012 417555 806626 301530 463616 466098 501604 351427 117147 277712 528711 809336 604581 460561 240195 269567 236425 961738 767283 113807 866150 410940 834428 982452 539951 098398 911207 577570 195825 043259 261896 664066 513758 888562 566477 591774 854812 557551 592043 687761 555889 414332 746680 279309 012490 474183 100976 555311 505287 514286 756358 440550 346152 633726 386431 735642 838342 037820 093207 761256 884831 384354 380142 199206 800384 763349 577321 106391 802086 824188 249779 947545 702953 398505 681869 403637 187930 066372 787864 566003 930284 990718 415076 101450 453411 771806 580763 047223 674674 399062 414743 606689 313578 558088 082816 256296 117724 136884 926277 430356 310610 828079 359945 755390 279002 385831 457722 215200 780763 188766 574828 971987 522308 916421 340305 906103 080831 167939 910302 024386 071760 372560 508261 430837 065125 755410 366569 241453 404900 865265 818277 766670 224394 878877 962798 217713 262419 063383 955166 693715 515254 639089 385846 626965 399645 680949 863827 417671 294614 242209 776931 587611 016304 998056 170950 871999 103407 590519 425726 973651 120802 235019 626002 931188 024790 667181 911924 428939 048380 628955 239158 214462 566836 242863 911526 206191 361894 100313 031144 642198 830675 553970 949292 512266 053589 878670 553576 492936 015145 651894 465134 328443 600082 404258 315632 370710 558705 794813 215566 518189 426790 037352 979138 716208 229824 254445 124008 758862 937470 945633 949880 241672 075393 870719 112379 511361 223418 377540 945521 639669 049416 533807 304359 470336 693607 155344 696769 412582 319968 928338 044673 602190 602528 828014 506003 282427 539821 806652 593093 640184 612592 341794 654276 819316 165451 938358 722502 056713 657780 315179 172448 705959 272019 263931 446236 137024 691855 893679 553534 404546 816227 820658 053813 458778 357736 653706 703355 264113 762729 267751 496558 617588 849621 785370 670757 024779 548502 081897 516933 001204 392123 261374 393599 978095 576735 626345 958494 676803 605937 133159 116192 280142 879326 646468 156362 866077 223480 892954 388567 911620 201979 050219 852236 280990 427945 904944 539824 398725 334329 014337 073928 008304 617882 157313 444316 199440 417228 826539 129041 289529 893964 481273 670396 629519 525709 475974 467819 089662 168270 515972 023610 491312 014853 332150 164471 638116 851244 890715 724836 111393 435143 592871 831117 101598 883219 166942 434986 783053 631781 465962 155355 271300 344311 812779 483776 924569 721442 539049 864852 311368 199894 403413 339549 446265 757849 579661 930308 746050 327442 342439 599560 615840 182840 022431 146953 003266 038715 316539 717370 934990 280749 495564 690509 419551 305261 778250 207186 369378 705669 761890 677055 152146 573747 452477 413377 822967 160444 773193 657272 605937 396489 286312 384748 520924 188275 145227 756059 003259 449596 838462 448604 728935 028090 864200 160847 855837 626999 024825 048457 404614 601933 091254 753923 794821 421891 537679 210730 266283 185096 706022 102760 701492 189917 915227 270457 758814 612869 156184 042843 599610 972116 593462 090815 386883 911874 902864 383243 389808 552090 595516 606026 373212 805233 853672 631370 907805 581805 945651 480277 242220 034916 701113 731281 248620 542823 733006 741328 594301 226374 016064 901140 406177 357736 999724 405821 991118 709813 883330 241168 342229 629435 718021 882332 817280 282830 895804 135183 498198 307372 228911 148260 287014 631351 206481 405391 560923 764983 467181 532561 111976 702792 178648 024870 620911 602938 498496 417681 217019 388343 465445 662723 117876 371384 734103 609056 276749 739309 950030 527910 136640 767365 099552 585363 178314 345942 834804 037849 500883 874432 925951 837337 297749 911560 746513 610425 359295 930310 151157 306931 044699 474838 218050 329245 186126 580706 126323 491889 131938 539816 124903 957312 545721 135128 581166 249371 894357 863510 029361 617989 481358 892074 877030 410389 532117 765111 883067 740523 512183 754679 666141 976016 450764 750975 159815 067367 308125 053195 749316 312550 796633 504871 664120 476065 057841 / 26 > 273443 [i]
- extracting embedded OOA [i] would yield OOA(273443, 1723, S27, 2, 3379), but