MinT - Best Known (59, 59+87, s)-Nets in Base 9

Best Known (59, 59+87, s)-Nets in Base 9

(59, 59+87, 92)-Net over F₉ — Constructive and digital

Digital (59, 146, 92)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 46, 28)-net over F₉, using
  - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [i]
2. digital (13, 100, 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]

(59, 59+87, 94)-Net in Base 9 — Constructive

(59, 146, 94)-net in base 9, using

1 times m-reduction [i] based on (59, 147, 94)-net in base 9, using
- base change [i] based on digital (10, 98, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(59, 59+87, 182)-Net over F₉ — Digital

Digital (59, 146, 182)-net over F₉, using

t-expansion [i] based on digital (50, 146, 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]

(59, 59+87, 3458)-Net in Base 9 — Upper bound on s

There is no (59, 146, 3459)-net in base 9, because

1 times m-reduction [i] would yield (59, 145, 3459)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 334205 757974 424186 405368 409277 405433 938910 457777 408100 744845 940509 226672 532734 702178 607262 689766 654577 506455 068343 489010 981727 206078 916233 > 9¹⁴⁵ [i]