Best Known (236, 236+∞, s)-Nets in Base 4
(236, 236+∞, 258)-Net over F4 — Constructive and digital
Digital (236, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (236, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 from the second 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) = 225 and N(F) ≥ 258, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
(236, 236+∞, 301)-Net over F4 — Digital
Digital (236, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (236, 300)-sequence over F4, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 234 and N(F) ≥ 301, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
(236, 236+∞, 726)-Net in Base 4 — Upper bound on s
There is no (236, m, 727)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (236, 3629, 727)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43629, 727, S4, 5, 3393), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16870 124245 403746 348392 898238 659075 019753 841418 523592 909856 746669 394490 895494 132509 741804 856552 301191 709580 259809 552904 755904 564323 863950 073037 305820 449273 559714 167740 033229 383706 634866 504856 315996 036395 864261 911937 802165 116854 099809 177473 608714 654855 726484 271118 628078 442167 386762 223347 032464 247072 671297 890822 982568 352619 405781 294926 812646 645953 505057 678061 697157 946270 017881 956028 789700 986990 822887 975067 059647 161362 953375 294954 774193 506292 254739 633449 290574 225828 401669 362163 452799 069205 998026 524887 742256 533653 844437 925888 588352 976490 183582 945062 880674 521795 770238 138913 039637 753278 308170 383926 022311 841676 410825 123508 425455 354411 986497 979451 316911 265854 303935 277760 271695 314196 851970 361485 426187 871827 778278 130037 664150 896511 503223 196907 207363 695877 624685 074663 884844 976393 667396 460273 238645 185283 139858 851383 825589 021563 761025 382659 227922 770407 956327 048221 905647 948877 892339 743254 215443 427151 748594 848669 369793 817859 770516 626638 376688 778233 012698 139239 519872 134543 389499 052479 611562 386379 044327 868944 326833 614354 965166 946795 560385 159581 064215 849723 043260 623111 811563 981940 990921 738333 280260 392495 901949 921863 544868 844439 357535 281921 507548 256191 086186 050707 618380 814404 526038 120088 667955 893681 622994 781477 536860 092726 826092 085144 101604 609188 496734 694164 663646 185439 571975 258809 951314 474051 156154 928108 727995 621723 011458 210983 063058 771539 438890 292401 736176 362031 895792 822102 256409 136128 375352 501604 832307 803786 962476 612753 869385 921565 577823 263099 143531 130560 727002 525960 489545 233515 638032 027711 512190 760159 072081 709044 081619 867934 330387 396355 159360 569527 982469 924546 100575 504150 965257 795893 520805 259502 888715 545033 949357 768714 419642 535543 071399 330623 999243 523640 621883 297985 192361 211563 862789 213422 971443 678454 511370 862822 222907 664055 637839 011458 731376 945194 685455 432850 738169 236536 481479 102026 806295 110137 404259 810878 956035 458020 083963 692028 222250 267057 285148 445118 695072 162032 318134 509224 850477 614121 449473 164689 527620 500734 928374 202625 990466 085673 821043 328976 833106 576397 611605 226302 486237 692673 296060 681485 087399 576562 757330 382242 143979 330225 843951 626722 026403 694935 979215 194363 116845 117514 496568 613232 487440 411831 413110 199470 980577 267597 205503 599332 013377 170047 253276 298286 465024 / 1697 > 43629 [i]
- extracting embedded OOA [i] would yield OOA(43629, 727, S4, 5, 3393), but