MinT - Best Known (58, 58+51, s)-Nets in Base 9

Best Known (58, 58+51, s)-Nets in Base 9

(58, 58+51, 232)-Net over F₉ — Constructive and digital

Digital (58, 109, 232)-net over F₉, using

3 times m-reduction [i] based on digital (58, 112, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 56, 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]

(58, 58+51, 281)-Net over F₉ — Digital

Digital (58, 109, 281)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+51, 16845)-Net in Base 9 — Upper bound on s

There is no (58, 109, 16846)-net in base 9, because

1 times m-reduction [i] would yield (58, 108, 16846)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 448935 111342 817900 078570 510048 647923 119747 241406 389417 003250 206257 965451 024467 093504 341701 879008 283633 > 9¹⁰⁸ [i]