Best Known (95−83, 95, s)-Nets in Base 27
(95−83, 95, 96)-Net over F27 — Constructive and digital
Digital (12, 95, 96)-net over F27, using
- t-expansion [i] based on digital (11, 95, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(95−83, 95, 109)-Net over F27 — Digital
Digital (12, 95, 109)-net over F27, using
- net from sequence [i] based on digital (12, 108)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 12 and N(F) ≥ 109, using
(95−83, 95, 1162)-Net over F27 — Upper bound on s (digital)
There is no digital (12, 95, 1163)-net over F27, because
- 1 times m-reduction [i] would yield digital (12, 94, 1163)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(2794, 1163, F27, 82) (dual of [1163, 1069, 83]-code), but
- the Johnson bound shows that N ≤ 1 306489 657127 071473 788851 765080 336082 748368 420876 859016 487906 677542 582351 942966 627757 264555 851783 232161 166756 964124 844019 874083 499953 208936 712476 218738 175530 357525 497690 717184 142421 606022 606350 042574 559739 514737 078202 571635 063720 814498 752817 683434 738402 499437 362360 309215 262817 890353 833447 429056 865908 468289 705443 607850 493134 115914 714422 143752 909297 809918 558684 437716 427208 700766 469952 701135 921822 903797 123365 819425 201797 881741 249100 083996 831323 718623 112116 692544 160535 235599 043790 775220 369903 105625 427770 412504 449393 747526 092645 820886 957758 509034 343876 646395 135476 204362 491734 960589 439469 997910 892987 247420 923766 216460 548971 559531 824590 200913 259201 654277 327079 172714 471645 309230 587655 892300 647524 299070 428024 883747 324571 402609 378368 312535 193889 768090 272326 778686 687986 646860 575712 514469 123324 614525 330947 218065 227826 439171 066758 136216 918415 943620 429877 663938 097024 968132 002523 617252 266903 339744 259172 344855 054369 403655 879658 815880 117117 234351 383829 361174 645848 077914 000413 326711 912996 292665 083464 518860 962333 315436 085294 645015 035200 760477 324128 138044 883890 165060 076306 149507 640228 372638 376485 307591 779428 743943 585455 052176 639335 926991 600210 616713 788002 340643 155676 580547 404978 298341 035563 608888 360641 373331 959234 274632 106368 204436 573364 471249 272410 298362 702734 396317 809057 868966 867705 690041 644676 331063 497651 655935 746445 763876 268609 949764 445524 328380 199206 851661 476214 799561 715601 051353 048367 826013 153691 634978 035922 700380 257129 915564 965017 836456 245195 862670 772463 609017 157138 202348 931144 325419 709228 962097 855639 122944 598456 413092 < 271069 [i]
- extracting embedded orthogonal array [i] would yield linear OA(2794, 1163, F27, 82) (dual of [1163, 1069, 83]-code), but
(95−83, 95, 1165)-Net in Base 27 — Upper bound on s
There is no (12, 95, 1166)-net in base 27, because
- 1 times m-reduction [i] would yield (12, 94, 1166)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 354 256200 763550 425061 685390 656095 041642 612926 419969 875481 475102 559259 393212 988689 038220 209355 614748 489371 463885 955331 058600 692017 154973 > 2794 [i]