MinT - Best Known (17, 17+56, s)-Nets in Base 64

Best Known (17, 17+56, s)-Nets in Base 64

(17, 17+56, 177)-Net over F₆₄ — Constructive and digital

Digital (17, 73, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 73, 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+56, 216)-Net in Base 64 — Constructive

(17, 73, 216)-net in base 64, using

11 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]

(17, 17+56, 267)-Net over F₆₄ — Digital

Digital (17, 73, 267)-net over F₆₄, using

t-expansion [i] based on digital (16, 73, 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+56, 9161)-Net in Base 64 — Upper bound on s

There is no (17, 73, 9162)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 710576 244545 776496 498908 956849 547306 056521 549761 349532 483219 247883 642671 587431 553036 144724 049268 421637 717091 804545 172386 289382 416976 > 64⁷³ [i]