MinT - Best Known (39−31, 39, s)-Nets in Base 64

Best Known (39−31, 39, s)-Nets in Base 64

(39−31, 39, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 39, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 39, 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]

(39−31, 39, 3830)-Net in Base 64 — Upper bound on s

There is no (8, 39, 3831)-net in base 64, because

1 times m-reduction [i] would yield (8, 38, 3831)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 432 098172 360142 599811 832565 215293 096936 693778 556928 524831 645021 910768 > 64³⁸ [i]