MinT - Best Known (99, 242, s)-Nets in Base 4

Best Known (99, 242, s)-Nets in Base 4

(99, 242, 104)-Net over F₄ — Constructive and digital

Digital (99, 242, 104)-net over F₄, using

t-expansion [i] based on digital (73, 242, 104)-net over F₄, using
- net from sequence [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]

(99, 242, 144)-Net over F₄ — Digital

Digital (99, 242, 144)-net over F₄, using

t-expansion [i] based on digital (91, 242, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(99, 242, 947)-Net in Base 4 — Upper bound on s

There is no (99, 242, 948)-net in base 4, because

1 times m-reduction [i] would yield (99, 241, 948)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 941176 287989 610992 004735 205086 477195 103161 924973 065228 413492 614450 841307 300566 884494 679515 087622 089138 917433 652954 777267 093467 547670 995860 097720 > 4²⁴¹ [i]