Best Known (237, 237+∞, s)-Nets in Base 4
(237, 237+∞, 258)-Net over F4 — Constructive and digital
Digital (237, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (237, 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
(237, 237+∞, 301)-Net over F4 — Digital
Digital (237, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (237, 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
(237, 237+∞, 729)-Net in Base 4 — Upper bound on s
There is no (237, m, 730)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (237, 3644, 730)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43644, 730, S4, 5, 3407), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 754084 492866 100778 104209 375418 593529 015236 400009 335373 356587 375285 572745 491990 699592 958691 015329 564908 267283 674245 481688 316630 942060 284469 640052 952962 370579 899203 173090 676629 520565 749434 676360 882982 934291 870415 406271 797492 772853 434700 369311 795702 670226 960297 509512 089410 420341 746704 507841 809957 402282 633653 295037 699171 818420 774942 676554 359014 441697 008982 006981 538023 141994 608293 571578 041887 663580 953715 966247 552237 263971 134942 435921 381097 094515 272080 508980 946079 757668 365302 774353 194076 615934 628976 538431 802804 858437 468884 701535 812545 902662 195634 340091 148098 632386 572353 972326 230710 322641 686369 523617 074447 897410 094373 431255 543009 495053 196610 266230 070767 446244 591542 476021 541190 836710 247964 493744 715413 979382 879171 067487 261752 788711 016110 712379 757518 583046 552959 947817 874748 299243 637716 985169 648227 341049 807339 195246 300724 416095 813422 722403 126972 950093 012218 187307 827556 435242 939774 340995 424836 598406 599868 913676 831885 445264 914320 825553 492069 648794 769620 066838 776392 014334 458537 153922 858508 045627 782912 019981 478611 162180 856834 194665 428560 297002 728144 853810 947984 655546 244561 519812 608203 512906 380559 293247 008171 817970 740741 373223 388076 395400 478477 926827 463163 154777 141522 810876 018699 680823 572727 812871 518831 999143 841201 081455 304631 624463 158832 994704 697546 135364 157315 874338 108546 375264 189499 577851 526667 842713 309345 356867 458745 683761 507093 199812 076396 667759 432880 385566 088424 005018 803696 772847 620478 933864 058654 704752 899788 467625 204272 478402 986517 042705 937690 869263 955450 511549 014936 637926 266726 894346 754165 058813 621059 493879 678439 534678 003825 769622 207435 117530 817441 563437 208271 031780 342911 579580 960426 175589 600784 637118 565235 417830 439080 253863 408923 077885 731323 738822 529451 084535 255245 257804 490148 278035 027147 904181 231756 649733 759162 517833 732103 528460 442831 509313 079798 809517 816058 753317 456662 015508 266138 594636 607899 316445 505451 520501 111258 251083 142176 223990 605404 002684 696926 521483 148145 634845 389688 032732 308520 708493 085715 675618 247389 982762 026461 507027 969686 832239 837017 586699 687890 191727 367138 751189 620910 481859 729428 379618 287198 503532 617473 030829 086174 653000 794591 290714 137274 051937 208620 992927 504409 747107 323967 220536 352109 051288 120048 848191 458814 765907 183684 652434 268283 265169 279718 260736 / 71 > 43644 [i]
- extracting embedded OOA [i] would yield OOA(43644, 730, S4, 5, 3407), but