Best Known (181, 181+∞, s)-Nets in Base 4
(181, 181+∞, 200)-Net over F4 — Constructive and digital
Digital (181, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (181, 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
(181, 181+∞, 220)-Net over F4 — Digital
Digital (181, m, 220)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (181, 219)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 181 and N(F) ≥ 220, using
(181, 181+∞, 560)-Net in Base 4 — Upper bound on s
There is no (181, m, 561)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (181, 2799, 561)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42799, 561, S4, 5, 2618), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 18 169267 215220 402407 221791 291833 479808 934047 145314 114005 698694 532067 772934 260658 256197 519569 619796 911572 262736 955046 321290 920516 464707 912251 952770 385828 412660 887324 566469 473250 588939 663555 870908 859498 388196 660552 915075 182771 608323 790211 239002 845506 538493 830492 297211 879206 648139 687469 344023 354180 057692 538924 519011 954443 786187 129640 635864 933177 781820 045081 334718 095366 439716 006644 208490 585600 144972 608124 511334 240036 331053 081387 572902 241558 549737 938580 826661 750710 021677 723067 605384 052311 950268 945099 528373 811467 727289 050781 596583 953250 963286 030879 207111 919384 817329 289925 524015 507606 090687 646370 871150 484929 806701 348132 710946 635666 470166 195152 728502 021591 375078 372199 792057 367178 392299 951098 671131 745618 644536 652117 039928 726861 506873 764827 561495 486506 003885 025800 510388 024611 987214 288417 774787 203981 858579 170354 024853 175049 158689 294945 487357 967315 564982 031811 171493 393693 733482 428207 035323 906285 596893 726332 833037 726374 042365 834810 212334 192698 329783 855107 214179 654977 105766 668375 016054 231216 765604 260727 058358 752340 902492 328640 031017 606105 158752 327851 334815 930998 251658 287003 231482 864323 706062 733018 668902 208844 825356 211858 589086 223138 205186 458356 715938 990801 846058 037121 804094 803943 895126 860714 523471 189418 453198 800155 154645 229098 834294 598927 952203 484894 595518 766761 872775 004933 502812 262953 900514 897319 585444 819778 031848 887599 364194 526846 791535 994610 486960 543995 669600 011385 112015 393789 881913 666113 553790 651610 932675 160751 069561 615821 923941 265776 496178 805399 446480 548158 746087 017193 186235 075043 565740 434020 263472 625824 353807 443523 151772 460475 494764 828303 342201 503463 547153 640318 408182 795521 884615 395816 640158 133833 139964 858371 904494 743615 858725 355810 973698 977498 780670 341827 601583 046656 / 97 > 42799 [i]
- extracting embedded OOA [i] would yield OOA(42799, 561, S4, 5, 2618), but