MinT - Best Known (59−51, 59, s)-Nets in Base 64

Best Known (59−51, 59, s)-Nets in Base 64

(59−51, 59, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 59, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 59, 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]

(59−51, 59, 2491)-Net in Base 64 — Upper bound on s

There is no (8, 59, 2492)-net in base 64, because

1 times m-reduction [i] would yield (8, 58, 2492)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 575 961316 933572 217291 691074 729530 781399 982491 286530 349438 229884 902813 227816 205147 840458 058814 149164 026611 > 64⁵⁸ [i]