Best Known (178, ∞, s)-Nets in Base 4
(178, ∞, 200)-Net over F4 — Constructive and digital
Digital (178, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (178, 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
(178, ∞, 215)-Net over F4 — Digital
Digital (178, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (178, 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
(178, ∞, 551)-Net in Base 4 — Upper bound on s
There is no (178, m, 552)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (178, 2754, 552)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42754, 552, S4, 5, 2576), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 132566 606720 110371 045487 070598 624956 199005 049457 646262 131055 940377 351359 113157 683458 171019 661239 476340 780240 102201 043068 596917 818029 690020 515784 962239 636402 713962 997516 026792 484062 411876 879796 497094 948934 371845 290692 624428 365690 755399 220250 705291 482903 915619 689832 701629 128648 018543 479843 614206 862552 288160 363660 779234 151577 019131 958678 346348 465429 182686 421911 944165 279155 255149 561542 150171 791737 719868 266707 304103 150121 464105 974744 775427 183848 621602 503201 598277 069920 751664 365156 231552 268444 182066 111675 338540 765202 762821 169397 639335 582136 487554 640440 690207 038037 501298 732677 494205 130971 463221 655246 729962 305970 632095 361607 068079 112191 173478 406941 671580 835994 833256 907325 794586 581427 966424 837376 131551 313800 982512 824984 832572 976866 111928 449189 592122 592955 880736 767812 957553 774615 448199 124327 853567 749709 438880 352472 538059 306641 658178 405892 379047 692038 277998 423914 520398 388553 601891 908904 734156 313588 325734 161261 323584 756498 794566 088673 472917 413483 016556 173754 021871 959219 459542 483881 880387 275743 970595 235101 536679 081018 714282 178658 434419 466097 576499 305079 556406 442618 480970 013109 587454 730996 928402 172659 887227 398416 685922 918997 985920 871194 081448 126735 197511 890169 428452 515168 247656 963030 721147 735533 404210 769532 471427 973910 105971 285938 232721 661582 492479 100215 396073 152887 593608 412904 683452 115904 875796 071567 832977 711864 600530 367899 563225 621632 461265 575393 267662 457053 444530 584290 339175 809634 834268 879256 163078 157408 278673 888025 451534 367061 424007 954828 970138 659595 416460 647876 584680 441142 830999 194592 840008 280914 745206 061644 131433 451674 302392 131074 195677 343059 965971 502298 732808 029510 652256 522686 884411 600791 674221 404694 776054 546360 753845 567416 454165 574681 886720 / 859 > 42754 [i]
- extracting embedded OOA [i] would yield OOA(42754, 552, S4, 5, 2576), but