Best Known (256, ∞, s)-Nets in Base 4
(256, ∞, 258)-Net over F4 — Constructive and digital
Digital (256, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (256, 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
(256, ∞, 301)-Net over F4 — Digital
Digital (256, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (256, 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
(256, ∞, 786)-Net in Base 4 — Upper bound on s
There is no (256, m, 787)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (256, 3929, 787)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43929, 787, S4, 5, 3673), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 68756 131839 181917 294865 025660 186322 994111 588232 667826 196820 192070 286194 037361 529411 326818 120733 670718 777930 076774 446790 537541 509026 030712 451260 893142 121676 751683 046986 383633 137055 295823 510964 798755 428414 903570 204640 533105 334973 584327 854948 922273 048643 493163 685843 578158 142378 621134 932998 733903 671482 508797 256446 308566 881076 242207 044105 261959 576130 956885 184313 387725 316980 597222 347491 672466 285118 331403 672827 251397 410315 350413 753816 207506 302920 961988 542804 834956 290377 099073 843495 497439 526465 448477 134485 986980 102609 610006 499330 910306 694375 048346 963103 661486 045727 868167 007571 851536 877072 561095 944034 571728 302789 731820 077524 951876 028794 945056 720165 700074 781253 485621 544106 501118 881328 255274 154069 021433 262213 701289 154241 973635 818977 866568 188567 054427 500722 657782 479080 826428 417188 337294 024979 881393 842412 701065 650199 105341 722644 625977 680502 544264 884493 727802 378743 474516 386842 812675 975746 134747 287864 548542 121531 906557 893459 509014 751218 981393 105396 753761 224387 214169 797892 639437 966047 540531 080251 468152 477456 313402 022619 283503 487040 419610 517791 451584 877855 532873 463304 561453 084033 207612 435966 038379 626805 312644 417364 155951 408502 540097 454490 075898 099703 891730 641202 992716 339460 608357 888451 253509 303845 756589 532557 155756 042437 369820 454289 806353 922913 784890 753397 343979 595058 814847 950404 591555 439225 914316 883000 069237 039796 689090 759762 757674 533523 301065 880413 783451 256052 539965 625402 209500 990301 862112 832412 282463 630926 123684 309600 827749 934285 022199 110612 639353 649797 018785 307915 394762 794520 678457 365172 172231 995082 107976 162037 560675 670796 160646 636691 941508 243315 356093 797637 816463 679846 475581 242152 135791 930890 129503 718124 537920 205775 437335 185680 625773 584477 101467 143846 630172 025833 539927 551488 028155 152133 146357 638113 511726 365744 381436 242135 071054 075003 718622 497607 745895 855672 644254 525875 552017 052052 579487 478110 282660 075434 348931 917715 745518 191159 871195 999726 589652 372515 766866 624363 339111 388747 123359 988031 734537 322193 273259 070518 155320 113656 115546 254636 603645 776275 891061 172116 648852 075428 389011 505225 316462 250305 085274 487076 160291 105591 603703 028650 673681 307885 398157 714149 315107 966781 182203 653638 322684 154483 153723 333943 646285 145763 493333 459721 873402 532393 313622 160344 744877 275484 282328 358064 805656 249627 189735 913999 657799 096666 287876 246911 614049 278457 958150 923914 852366 814562 683202 384636 355430 483801 967785 215058 685193 432886 317464 640390 904024 855383 913859 803212 939264 / 1837 > 43929 [i]
- extracting embedded OOA [i] would yield OOA(43929, 787, S4, 5, 3673), but