MinT - Best Known (32−24, 32, s)-Nets in Base 64

Best Known (32−24, 32, s)-Nets in Base 64

(32−24, 32, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 32, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 32, 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]

(32−24, 32, 257)-Net in Base 64 — Constructive

(8, 32, 257)-net in base 64, using

base change [i] based on digital (0, 24, 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]

(32−24, 32, 5496)-Net in Base 64 — Upper bound on s

There is no (8, 32, 5497)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 6289 982488 974287 478184 449774 810980 334979 814739 298016 243380 > 64³² [i]