MinT - Best Known (113−63, 113, s)-Nets in Base 9

Best Known (113−63, 113, s)-Nets in Base 9

(113−63, 113, 98)-Net over F₉ — Constructive and digital

Digital (50, 113, 98)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (6, 37, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
2. digital (13, 76, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(113−63, 113, 182)-Net over F₉ — Digital

Digital (50, 113, 182)-net over F₉, using

net from sequence [i] based on digital (50, 181)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
  - a curve from the manYPoints database [i]

(113−63, 113, 4331)-Net in Base 9 — Upper bound on s

There is no (50, 113, 4332)-net in base 9, because

1 times m-reduction [i] would yield (50, 112, 4332)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75260 620731 473287 792315 989892 819725 605044 343526 594426 177481 205369 300520 820699 489659 834951 124211 648416 810017 > 9¹¹² [i]