MinT - Best Known (76−59, 76, s)-Nets in Base 64

Best Known (76−59, 76, s)-Nets in Base 64

(76−59, 76, 177)-Net over F₆₄ — Constructive and digital

Digital (17, 76, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 76, 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]

(76−59, 76, 216)-Net in Base 64 — Constructive

(17, 76, 216)-net in base 64, using

8 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]

(76−59, 76, 267)-Net over F₆₄ — Digital

Digital (17, 76, 267)-net over F₆₄, using

t-expansion [i] based on digital (16, 76, 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]

(76−59, 76, 8673)-Net in Base 64 — Upper bound on s

There is no (17, 76, 8674)-net in base 64, because

1 times m-reduction [i] would yield (17, 75, 8674)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2908 519762 984794 468213 043319 791167 800222 808042 500304 169943 406451 465774 323945 624690 011321 463228 340945 759201 431354 254155 350680 701816 062328 > 64⁷⁵ [i]