MinT - Best Known (31, 31+100, s)-Nets in Base 9

Best Known (31, 31+100, s)-Nets in Base 9

(31, 31+100, 78)-Net over F₉ — Constructive and digital

Digital (31, 131, 78)-net over F₉, using

t-expansion [i] based on digital (22, 131, 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+100, 120)-Net over F₉ — Digital

Digital (31, 131, 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+100, 739)-Net in Base 9 — Upper bound on s

There is no (31, 131, 740)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101659 782049 610659 204706 265004 666546 388564 146111 628774 821820 735250 676812 692320 268341 136906 703120 108118 396592 917631 918128 813761 > 9¹³¹ [i]