MinT - Best Known (40, 115, s)-Nets in Base 9

Best Known (40, 115, s)-Nets in Base 9

(40, 115, 81)-Net over F₉ — Constructive and digital

Digital (40, 115, 81)-net over F₉, using

t-expansion [i] based on digital (32, 115, 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]

(40, 115, 140)-Net over F₉ — Digital

Digital (40, 115, 140)-net over F₉, using

t-expansion [i] based on digital (39, 115, 140)-net over F₉, using
- net from sequence [i] based on digital (39, 139)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
    - a curve from the manYPoints database [i]

(40, 115, 1573)-Net in Base 9 — Upper bound on s

There is no (40, 115, 1574)-net in base 9, because

1 times m-reduction [i] would yield (40, 114, 1574)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 210927 529588 700656 975185 038169 241561 028931 544540 320055 161739 142730 636635 574016 740254 621412 207214 641150 119025 > 9¹¹⁴ [i]