MinT - Best Known (86, 244, s)-Nets in Base 4

Best Known (86, 244, s)-Nets in Base 4

(86, 244, 104)-Net over F₄ — Constructive and digital

Digital (86, 244, 104)-net over F₄, using

t-expansion [i] based on digital (73, 244, 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]

(86, 244, 129)-Net over F₄ — Digital

Digital (86, 244, 129)-net over F₄, using

t-expansion [i] based on digital (81, 244, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(86, 244, 665)-Net in Base 4 — Upper bound on s

There is no (86, 244, 666)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 805 091760 550563 944388 673483 563702 436388 631996 364352 724363 020851 639756 308471 590663 334226 132138 893101 659172 351683 753817 586822 831787 444791 226085 311408 > 4²⁴⁴ [i]