MinT - Best Known (38, 105, s)-Nets in Base 9

Best Known (38, 105, s)-Nets in Base 9

(38, 105, 81)-Net over F₉ — Constructive and digital

Digital (38, 105, 81)-net over F₉, using

t-expansion [i] based on digital (32, 105, 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]

(38, 105, 128)-Net over F₉ — Digital

Digital (38, 105, 128)-net over F₉, using

t-expansion [i] based on digital (33, 105, 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]

(38, 105, 1653)-Net in Base 9 — Upper bound on s

There is no (38, 105, 1654)-net in base 9, because

1 times m-reduction [i] would yield (38, 104, 1654)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1768 786233 447557 356242 891580 014843 983853 580273 538435 705333 812652 933837 304256 577212 823975 464077 811121 > 9¹⁰⁴ [i]