MinT - Best Known (70−59, 70, s)-Nets in Base 64

Best Known (70−59, 70, s)-Nets in Base 64

(70−59, 70, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 70, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 70, 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]

(70−59, 70, 225)-Net over F₆₄ — Digital

Digital (11, 70, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 70, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(70−59, 70, 3660)-Net in Base 64 — Upper bound on s

There is no (11, 70, 3661)-net in base 64, because

1 times m-reduction [i] would yield (11, 69, 3661)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 42495 094817 505927 146094 556066 435514 926594 113436 435284 802283 452622 736942 653605 049568 443861 547343 023818 415558 023579 443434 521152 > 64⁶⁹ [i]