Best Known (126, 126+∞, s)-Nets in Base 4
(126, 126+∞, 130)-Net over F4 — Constructive and digital
Digital (126, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (126, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
(126, 126+∞, 176)-Net over F4 — Digital
Digital (126, m, 176)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (126, 175)-sequence over F4, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 125 and N(F) ≥ 176, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
(126, 126+∞, 394)-Net in Base 4 — Upper bound on s
There is no (126, m, 395)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (126, 1969, 395)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(41969, 395, S4, 5, 1843), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 574978 115548 578937 518260 117586 162661 814155 184358 459578 010163 524345 466919 542234 926063 964963 397420 584027 452767 146934 167729 424970 270745 605456 125295 687515 268156 742653 201449 802126 526893 603470 013339 193488 662777 240120 524445 265699 334971 674345 405832 048669 181258 758780 816443 677765 254719 031298 669718 084911 652590 313537 086555 202031 606336 724760 788362 019583 332760 032531 628110 012675 550469 918522 252178 286634 779078 241540 246140 069943 483417 925186 906805 337543 214267 638709 612234 992399 803754 018766 876004 275329 698061 591858 548992 326898 041203 931533 188100 828525 671260 378525 586858 535989 921401 185656 800395 360246 016422 892002 962888 245006 973866 304141 906439 434686 400972 605922 839020 304514 434856 908076 573914 475126 982770 556805 967581 773017 684520 158553 622898 228941 361413 910581 243258 974906 353509 286684 441708 332260 156713 667460 400834 600975 694970 539593 074206 896376 486965 238201 335496 918924 878411 107807 066082 751234 348784 068493 407895 268688 059882 450278 751668 841543 346777 542825 959077 648090 603687 811738 685152 183020 413770 692149 570405 295046 916082 755169 750443 521080 389969 300061 952147 619055 639575 890813 642084 472829 491106 127680 703658 955446 302370 025212 064802 741954 311839 966775 566486 152770 598012 014515 745700 575398 170181 333364 864037 816729 862144 / 461 > 41969 [i]
- extracting embedded OOA [i] would yield OOA(41969, 395, S4, 5, 1843), but