MinT - Best Known (149−95, 149, s)-Nets in Base 9

Best Known (149−95, 149, s)-Nets in Base 9

(149−95, 149, 81)-Net over F₉ — Constructive and digital

Digital (54, 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]

(149−95, 149, 182)-Net over F₉ — Digital

Digital (54, 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]

(149−95, 149, 2293)-Net in Base 9 — Upper bound on s

There is no (54, 149, 2294)-net in base 9, because

1 times m-reduction [i] would yield (54, 148, 2294)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1717 345767 287524 443614 262537 267278 520945 592970 642476 456927 334201 537315 864874 258062 218811 071983 875612 327164 846626 529707 977691 820649 753432 906385 > 9¹⁴⁸ [i]