MinT - Best Known (17, 17+74, s)-Nets in Base 64

Best Known (17, 17+74, s)-Nets in Base 64

(17, 17+74, 177)-Net over F₆₄ — Constructive and digital

Digital (17, 91, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 91, 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]

(17, 17+74, 192)-Net in Base 64 — Constructive

(17, 91, 192)-net in base 64, using

t-expansion [i] based on (16, 91, 192)-net in base 64, using
- base change [i] based on digital (3, 78, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(17, 17+74, 267)-Net over F₆₄ — Digital

Digital (17, 91, 267)-net over F₆₄, using

t-expansion [i] based on digital (16, 91, 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]

(17, 17+74, 6420)-Net in Base 64 — Upper bound on s

There is no (17, 91, 6421)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 231 517872 012540 301048 139421 422546 829154 206005 027582 232432 859702 752464 744669 592625 073000 897495 480567 352164 058415 445856 416420 226432 633575 306757 193489 811188 119129 073792 > 64⁹¹ [i]