Best Known (166, 166+∞, s)-Nets in Base 4
(166, 166+∞, 200)-Net over F4 — Constructive and digital
Digital (166, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (166, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
(166, 166+∞, 215)-Net over F4 — Digital
Digital (166, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (166, 214)-sequence over F4, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 148 and N(F) ≥ 215, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
(166, 166+∞, 515)-Net in Base 4 — Upper bound on s
There is no (166, m, 516)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (166, 2574, 516)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42574, 516, S4, 5, 2408), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 57252 704879 096151 632512 726171 646350 874272 374060 915829 584223 662592 148716 629659 986196 310235 384941 235901 407118 723960 020565 916271 692965 907444 786589 380715 607427 173176 221755 028348 183453 318389 048447 629814 317190 390949 237468 256584 598516 103936 557877 044605 190395 309934 312362 186976 550066 838856 264130 720217 929426 309173 872650 512649 549496 126704 872631 399947 875967 104646 628914 848623 396417 770902 684367 663668 739396 684698 636034 651295 574835 527969 945158 428272 931164 351005 615024 124283 163598 639129 582517 041628 985718 615419 892259 075011 637078 320015 318776 088291 756073 250355 585959 940210 410696 733445 494232 008525 166589 198105 458504 319346 989203 098156 465404 395592 297454 770181 443644 772886 688047 189261 111927 054777 578692 712800 991889 355963 895381 164731 069334 834229 850064 074199 574113 187235 004714 569129 447933 245533 648341 105811 643111 687205 875043 915053 300619 085206 024517 133459 807287 266926 791740 778638 555295 717882 475553 415441 499629 192885 258082 630854 128042 748375 776877 113171 847397 350728 231185 669928 711197 546502 171655 854331 785265 282531 439148 538181 262300 484555 508481 752478 814769 198485 567559 864637 482956 307518 490113 007958 221836 553202 544168 672544 616529 252893 421327 204670 797283 212948 316504 676574 311627 551479 758861 960646 331015 486834 274466 588069 007895 933942 054861 236028 055159 329443 467183 938343 189176 976392 642735 399928 041990 636345 289532 479485 429865 500551 102894 149718 879402 990177 900134 363700 450164 271511 095090 752195 013672 406099 652919 997713 754080 368646 595106 216386 637045 484627 373375 306438 925763 186066 976627 402836 706886 261736 686841 444056 791386 447798 625093 809420 886766 231880 212123 680427 568618 413610 776936 841216 / 803 > 42574 [i]
- extracting embedded OOA [i] would yield OOA(42574, 516, S4, 5, 2408), but