MinT - Best Known (76−67, 76, s)-Nets in Base 64

Best Known (76−67, 76, s)-Nets in Base 64

(76−67, 76, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 76, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 76, 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]

(76−67, 76, 209)-Net over F₆₄ — Digital

Digital (9, 76, 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]

(76−67, 76, 2644)-Net in Base 64 — Upper bound on s

There is no (9, 76, 2645)-net in base 64, because

1 times m-reduction [i] would yield (9, 75, 2645)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2942 695364 284026 159441 082621 147248 107092 253307 302481 360808 750380 872537 348481 402779 023374 223496 675388 282014 765932 437824 359811 313619 246552 > 64⁷⁵ [i]