MinT - Best Known (81−64, 81, s)-Nets in Base 64

Best Known (81−64, 81, s)-Nets in Base 64

(81−64, 81, 177)-Net over F₆₄ — Constructive and digital

Digital (17, 81, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 81, 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]

(81−64, 81, 216)-Net in Base 64 — Constructive

(17, 81, 216)-net in base 64, using

3 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
- base change [i] based on digital (5, 72, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(81−64, 81, 267)-Net over F₆₄ — Digital

Digital (17, 81, 267)-net over F₆₄, using

t-expansion [i] based on digital (16, 81, 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]

(81−64, 81, 7559)-Net in Base 64 — Upper bound on s

There is no (17, 81, 7560)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 199 897356 604543 045287 171188 349251 498602 864963 418962 912133 802481 581527 956271 688414 179793 758965 988203 332607 069013 247643 522823 914963 972170 362757 191380 > 64⁸¹ [i]