MinT - Best Known (31, 31+102, s)-Nets in Base 9

Best Known (31, 31+102, s)-Nets in Base 9

(31, 31+102, 78)-Net over F₉ — Constructive and digital

Digital (31, 133, 78)-net over F₉, using

t-expansion [i] based on digital (22, 133, 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]

(31, 31+102, 120)-Net over F₉ — Digital

Digital (31, 133, 120)-net over F₉, using

net from sequence [i] based on digital (31, 119)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
  - a curve from the manYPoints database [i]

(31, 31+102, 733)-Net in Base 9 — Upper bound on s

There is no (31, 133, 734)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 586648 790587 663577 104822 766732 113972 004825 106247 939102 530679 261957 030787 584476 877320 830032 099031 104003 237145 325959 517221 680273 > 9¹³³ [i]