MinT - Best Known (149−91, 149, s)-Nets in Base 9

Best Known (149−91, 149, s)-Nets in Base 9

(149−91, 149, 81)-Net over F₉ — Constructive and digital

Digital (58, 149, 81)-net over F₉, using

t-expansion [i] based on digital (32, 149, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(149−91, 149, 84)-Net in Base 9 — Constructive

(58, 149, 84)-net in base 9, using

1 times m-reduction [i] based on (58, 150, 84)-net in base 9, using
- base change [i] based on digital (8, 100, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(149−91, 149, 182)-Net over F₉ — Digital

Digital (58, 149, 182)-net over F₉, using

t-expansion [i] based on digital (50, 149, 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]

(149−91, 149, 3002)-Net in Base 9 — Upper bound on s

There is no (58, 149, 3003)-net in base 9, because

1 times m-reduction [i] would yield (58, 148, 3003)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1697 120436 976402 586618 920120 598663 361609 034669 376759 357481 307735 860581 080005 259979 185393 328683 154124 314531 335554 524650 539632 296647 342552 510969 > 9¹⁴⁸ [i]