MinT - Best Known (142−83, 142, s)-Nets in Base 9

Best Known (142−83, 142, s)-Nets in Base 9

(142−83, 142, 96)-Net over F₉ — Constructive and digital

Digital (59, 142, 96)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 46, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]
2. digital (13, 96, 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]

(142−83, 142, 182)-Net over F₉ — Digital

Digital (59, 142, 182)-net over F₉, using

t-expansion [i] based on digital (50, 142, 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]

(142−83, 142, 3834)-Net in Base 9 — Upper bound on s

There is no (59, 142, 3835)-net in base 9, because

1 times m-reduction [i] would yield (59, 141, 3835)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 357 022651 503396 867612 941336 791745 879391 021063 222422 596867 760422 140195 564993 362756 862934 667336 688844 681731 136274 692676 572388 788008 174489 > 9¹⁴¹ [i]