MinT - Best Known (84−73, 84, s)-Nets in Base 64

Best Known (84−73, 84, s)-Nets in Base 64

(84−73, 84, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 84, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 84, 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]

(84−73, 84, 225)-Net over F₆₄ — Digital

Digital (11, 84, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 84, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(84−73, 84, 3290)-Net in Base 64 — Upper bound on s

There is no (11, 84, 3291)-net in base 64, because

1 times m-reduction [i] would yield (11, 83, 3291)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 822345 345147 037767 782903 835206 234015 957601 721572 176578 004677 253002 821198 991161 861240 583507 065993 768111 071585 815187 772764 675952 997919 487016 941259 989700 > 64⁸³ [i]