MinT - Best Known (149−111, 149, s)-Nets in Base 9

Best Known (149−111, 149, s)-Nets in Base 9

(149−111, 149, 81)-Net over F₉ — Constructive and digital

Digital (38, 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]

(149−111, 149, 128)-Net over F₉ — Digital

Digital (38, 149, 128)-net over F₉, using

t-expansion [i] based on digital (33, 149, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(149−111, 149, 952)-Net in Base 9 — Upper bound on s

There is no (38, 149, 953)-net in base 9, because

1 times m-reduction [i] would yield (38, 148, 953)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1748 162815 642187 717205 370402 068707 016363 207372 563411 734963 659512 721347 543142 587941 263820 390029 044837 481964 514885 840168 712283 892603 385648 877625 > 9¹⁴⁸ [i]