MinT - Best Known (48−25, 48, s)-Nets in Base 9

Best Known (48−25, 48, s)-Nets in Base 9

(48−25, 48, 78)-Net over F₉ — Constructive and digital

Digital (23, 48, 78)-net over F₉, using

t-expansion [i] based on digital (22, 48, 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]

(48−25, 48, 82)-Net in Base 9 — Constructive

(23, 48, 82)-net in base 9, using

base change [i] based on digital (7, 32, 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]

(48−25, 48, 96)-Net over F₉ — Digital

Digital (23, 48, 96)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(48−25, 48, 3604)-Net in Base 9 — Upper bound on s

There is no (23, 48, 3605)-net in base 9, because

1 times m-reduction [i] would yield (23, 47, 3605)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 707 472716 748656 595167 747025 629516 010029 347681 > 9⁴⁷ [i]