Best Known (188, ∞, s)-Nets in Base 4
(188, ∞, 200)-Net over F4 — Constructive and digital
Digital (188, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (188, 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
(188, ∞, 220)-Net over F4 — Digital
Digital (188, m, 220)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (188, 219)-sequence over F4, using
- t-expansion [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
- t-expansion [i] based on digital (181, 219)-sequence over F4, using
(188, ∞, 581)-Net in Base 4 — Upper bound on s
There is no (188, m, 582)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (188, 2904, 582)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42904, 582, S4, 5, 2716), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 800484 450478 726412 101832 111230 147500 359981 994539 812082 461704 553475 471788 856034 018939 502190 383446 494917 709219 411815 397890 386553 606398 363766 653759 317102 823979 534674 898591 151357 941496 849892 519684 443820 769487 829101 190497 409099 151288 416758 473881 737985 936766 101319 028713 172209 413295 292728 026793 152053 319681 864431 642911 822337 158200 841832 929867 515973 515134 868488 674946 650264 210562 280381 455816 375974 613974 587148 378340 310408 581018 022047 621527 107016 903970 353577 908106 069049 814590 792157 389687 890665 276959 512885 470376 007452 478786 241196 946028 179603 997539 605492 620368 752785 965807 613199 536893 614672 995613 441747 114088 372599 001545 846084 723076 889616 599593 253178 185410 956244 002797 892906 681090 938883 080227 730215 836736 626729 894383 923515 963725 817665 130814 760301 185507 312845 196851 473012 417460 387618 393098 791663 544364 882698 376538 108219 255712 594384 274644 069329 652888 375878 817659 810832 349817 908292 658860 475630 051983 246282 918219 678444 601667 465282 351882 534806 986424 865121 275867 018372 021792 984010 937103 346684 066691 289396 857443 740769 905494 047130 961087 171336 564934 173661 043762 566120 636661 607130 374061 483398 055696 750724 819983 177242 376336 302520 347850 020572 135967 575237 736847 440057 744281 099731 408165 405927 499574 199253 461144 084710 446000 450435 266164 848328 085261 509291 445932 112855 091176 838223 730296 266155 746114 026086 616818 594412 937447 534495 886504 932461 825911 145756 426717 744674 721715 007530 174849 805149 964101 720041 295949 366555 033480 501865 132860 762572 758773 415489 517746 642698 570384 497885 969789 839592 065447 460752 153367 897842 678736 934183 832690 891841 541017 910949 425660 636504 026607 552836 507645 212526 403465 299118 825672 039632 084878 444326 546257 730948 738093 914049 460445 149340 377548 980142 721543 798289 476873 946439 969472 373430 003105 282371 928824 326986 292471 699154 488834 096403 987638 192957 936398 338275 409920 / 2717 > 42904 [i]
- extracting embedded OOA [i] would yield OOA(42904, 582, S4, 5, 2716), but