MinT - Best Known (76, 76+∞, s)-Nets in Base 4

Best Known (76, 76+∞, s)-Nets in Base 4

Digital (76, m, 104)-net over F₄ for arbitrarily large m, using

net from sequence [i] based on digital (76, 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 (76, m, 112)-net over F₄ for arbitrarily large m, using

net from sequence [i] based on digital (76, 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 (76, m, 244)-net in base 4 for arbitrarily large m, because

m-reduction [i] would yield (76, 971, 244)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4⁹⁷¹, 244, S₄, 4, 895), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 3236 495064 695462 528997 413953 330229 044521 211312 867656 381645 225806 522239 318037 753863 540245 099467 700607 936753 395378 536418 356635 956923 923859 637702 464635 574553 912281 234181 061656 107072 908620 315468 285825 871829 605261 071265 318812 008756 154733 723871 390958 755099 634413 719116 956717 212607 293010 816930 491362 530484 772939 406717 161220 021235 772182 262698 194391 450125 569975 139422 526204 534737 413018 710952 618916 724816 624907 846650 319306 877262 588897 780323 560363 596760 137690 106380 084687 279408 518195 660212 098529 239184 091458 881742 690380 088164 118624 920996 164707 633911 978209 489079 977045 739070 188832 711685 553489 182720 / 7 > 4⁹⁷¹ [i]