MinT - Best Known (99, 99+31, s)-Nets in Base 9

Best Known (99, 99+31, s)-Nets in Base 9

(99, 99+31, 972)-Net over F₉ — Constructive and digital

Digital (99, 130, 972)-net over F₉, using

9² times duplication [i] based on digital (97, 128, 972)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (19, 34, 232)-net over F₉, using
    - trace code for nets [i] based on digital (2, 17, 116)-net over F₈₁, using
      - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]
  2. digital (63, 94, 740)-net over F₉, using
    - trace code for nets [i] based on digital (16, 47, 370)-net over F₈₁, using
      - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(99, 99+31, 20562)-Net over F₉ — Digital

Digital (99, 130, 20562)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+31, large)-Net in Base 9 — Upper bound on s

There is no (99, 130, large)-net in base 9, because

29 times m-reduction [i] would yield (99, 101, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]