MinT - Best Known (131−95, 131, s)-Nets in Base 9

Best Known (131−95, 131, s)-Nets in Base 9

(131−95, 131, 81)-Net over F₉ — Constructive and digital

Digital (36, 131, 81)-net over F₉, using

t-expansion [i] based on digital (32, 131, 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]

(131−95, 131, 128)-Net over F₉ — Digital

Digital (36, 131, 128)-net over F₉, using

t-expansion [i] based on digital (33, 131, 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]

(131−95, 131, 972)-Net in Base 9 — Upper bound on s

There is no (36, 131, 973)-net in base 9, because

1 times m-reduction [i] would yield (36, 130, 973)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11638 330213 182643 016740 342422 394640 280891 800200 428548 079916 620036 034607 844630 907136 376957 739596 716769 133278 075277 831459 196889 > 9¹³⁰ [i]