MinT - Best Known (88−79, 88, s)-Nets in Base 64

Best Known (88−79, 88, s)-Nets in Base 64

(88−79, 88, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 88, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 88, 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]

(88−79, 88, 209)-Net over F₆₄ — Digital

Digital (9, 88, 209)-net over F₆₄, using

net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
  - a curve from the manYPoints database [i]

(88−79, 88, 2594)-Net in Base 64 — Upper bound on s

There is no (9, 88, 2595)-net in base 64, because

1 times m-reduction [i] would yield (9, 87, 2595)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 13 913563 691894 496464 710890 382387 702477 105872 129735 853646 249780 756300 432234 792839 692079 885237 562267 741774 484856 501905 117145 361509 501416 262061 610404 176852 088320 > 64⁸⁷ [i]