MinT - Best Known (78, 78+∞, s)-Nets in Base 4

Best Known (78, 78+∞, s)-Nets in Base 4

Digital (78, m, 104)-net over F₄ for arbitrarily large m, using

net from sequence [i] based on digital (78, 103)-sequence over F₄, using
- t-expansion [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

Digital (78, m, 112)-net over F₄ for arbitrarily large m, using

net from sequence [i] based on digital (78, 111)-sequence over F₄, using
- t-expansion [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

There is no (78, m, 250)-net in base 4 for arbitrarily large m, because

m-reduction [i] would yield (78, 995, 250)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4⁹⁹⁵, 250, S₄, 4, 917), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 19 285007 772184 743961 723370 176031 377075 374867 652271 052195 522905 345120 292671 824970 115561 077309 222566 252536 397062 295492 538772 744576 295746 632520 044940 748111 752723 369490 364251 672031 365693 372555 945036 997827 580362 226205 178161 972409 354295 506775 906717 734582 893550 448640 628840 424939 918254 069540 628633 027584 159079 317569 528371 430983 264612 899679 088829 314581 016388 240306 434050 071816 057470 493553 461562 873225 525464 775937 045925 007992 107273 189585 591303 956537 839374 282258 772100 742002 280715 565212 327725 327670 016251 230918 197192 805859 766479 170777 335218 888977 905794 362729 324034 697436 436478 263211 871660 830134 811616 986716 438528 / 153 > 4⁹⁹⁵ [i]