MinT - Best Known (11, 78, s)-Nets in Base 64

Best Known (11, 78, s)-Nets in Base 64

(11, 78, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 78, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 78, 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]

(11, 78, 225)-Net over F₆₄ — Digital

Digital (11, 78, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 78, 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]

(11, 78, 3406)-Net in Base 64 — Upper bound on s

There is no (11, 78, 3407)-net in base 64, because

1 times m-reduction [i] would yield (11, 77, 3407)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 11 942830 498090 457055 170326 988617 661875 388782 393138 598882 895770 109959 739299 507719 012118 959481 523381 960591 942781 544493 886112 238970 754494 630732 > 64⁷⁷ [i]