MinT - Best Known (24, 51, s)-Nets in Base 9

Best Known (24, 51, s)-Nets in Base 9

(24, 51, 78)-Net over F₉ — Constructive and digital

Digital (24, 51, 78)-net over F₉, using

t-expansion [i] based on digital (22, 51, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(24, 51, 82)-Net in Base 9 — Constructive

(24, 51, 82)-net in base 9, using

base change [i] based on digital (7, 34, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(24, 51, 94)-Net over F₉ — Digital

Digital (24, 51, 94)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(24, 51, 3307)-Net in Base 9 — Upper bound on s

There is no (24, 51, 3308)-net in base 9, because

1 times m-reduction [i] would yield (24, 50, 3308)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 516690 607182 154048 016223 200278 480777 896663 726305 > 9⁵⁰ [i]