MinT - Best Known (64−48, 64, s)-Nets in Base 64

Best Known (64−48, 64, s)-Nets in Base 64

(64−48, 64, 177)-Net over F₆₄ — Constructive and digital

Digital (16, 64, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 64, 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]

(64−48, 64, 257)-Net in Base 64 — Constructive

(16, 64, 257)-net in base 64, using

base change [i] based on digital (0, 48, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(64−48, 64, 267)-Net over F₆₄ — Digital

Digital (16, 64, 267)-net over F₆₄, using

net from sequence [i] based on digital (16, 266)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 16 and N(F) ≥ 267, using
  - a curve from the manYPoints database [i]

(64−48, 64, 10185)-Net in Base 64 — Upper bound on s

There is no (16, 64, 10186)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 39 418779 853939 213772 621381 718927 418660 655675 820468 922201 437311 382444 130198 938963 284632 108134 076339 321096 250971 187356 > 64⁶⁴ [i]