MinT - Best Known (120−93, 120, s)-Nets in Base 9

Best Known (120−93, 120, s)-Nets in Base 9

(120−93, 120, 78)-Net over F₉ — Constructive and digital

Digital (27, 120, 78)-net over F₉, using

t-expansion [i] based on digital (22, 120, 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]

(120−93, 120, 110)-Net over F₉ — Digital

Digital (27, 120, 110)-net over F₉, using

t-expansion [i] based on digital (26, 120, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(120−93, 120, 633)-Net in Base 9 — Upper bound on s

There is no (27, 120, 634)-net in base 9, because

1 times m-reduction [i] would yield (27, 119, 634)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 361497 164623 367595 828819 479268 422930 767132 810656 500806 583819 519331 350072 614130 364844 342724 021002 678772 124042 852513 > 9¹¹⁹ [i]