MinT - Best Known (9, 9+72, s)-Nets in Base 64

Best Known (9, 9+72, s)-Nets in Base 64

(9, 9+72, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 81, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 81, 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]

(9, 9+72, 209)-Net over F₆₄ — Digital

Digital (9, 81, 209)-net over F₆₄, using

net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
  - a curve from the manYPoints database [i]

(9, 9+72, 2607)-Net in Base 64 — Upper bound on s

There is no (9, 81, 2608)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 199 808802 399326 747494 997277 422464 760503 731859 131976 355357 077518 957128 150558 055360 501127 565968 035843 855543 871991 285269 070788 538157 197243 484786 435745 > 64⁸¹ [i]