MinT - Best Known (70−60, 70, s)-Nets in Base 64

Best Known (70−60, 70, s)-Nets in Base 64

(70−60, 70, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 70, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 70, 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]

(70−60, 70, 225)-Net over F₆₄ — Digital

Digital (10, 70, 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]

(70−60, 70, 3117)-Net in Base 64 — Upper bound on s

There is no (10, 70, 3118)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2 724019 657928 497177 727841 226185 415911 688061 610094 955992 724455 532359 370606 469183 040968 193940 218709 551407 621358 102144 630083 512368 > 64⁷⁰ [i]