MinT - Best Known (44−36, 44, s)-Nets in Base 64

Best Known (44−36, 44, s)-Nets in Base 64

(44−36, 44, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 44, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 44, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(44−36, 44, 3109)-Net in Base 64 — Upper bound on s

There is no (8, 44, 3110)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 29 751969 958791 526352 108701 933580 213638 138144 203247 410853 880910 368814 309645 935068 > 64⁴⁴ [i]