MinT - Best Known (87−78, 87, s)-Nets in Base 64

Best Known (87−78, 87, s)-Nets in Base 64

(87−78, 87, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 87, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 87, 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]

(87−78, 87, 209)-Net over F₆₄ — Digital

Digital (9, 87, 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]

(87−78, 87, 2594)-Net in Base 64 — Upper bound on s

There is no (9, 87, 2595)-net in base 64, because

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]