MinT - Best Known (37, 37+111, s)-Nets in Base 9

Best Known (37, 37+111, s)-Nets in Base 9

(37, 37+111, 81)-Net over F₉ — Constructive and digital

Digital (37, 148, 81)-net over F₉, using

t-expansion [i] based on digital (32, 148, 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]

(37, 37+111, 128)-Net over F₉ — Digital

Digital (37, 148, 128)-net over F₉, using

t-expansion [i] based on digital (33, 148, 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]

(37, 37+111, 913)-Net in Base 9 — Upper bound on s

There is no (37, 148, 914)-net in base 9, because

1 times m-reduction [i] would yield (37, 147, 914)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 190 018703 803277 754103 405627 539949 890528 040933 193542 807994 311283 861283 036117 556416 558897 224833 494723 909967 700975 239586 853221 852128 348235 232945 > 9¹⁴⁷ [i]