MinT - Best Known (131−93, 131, s)-Nets in Base 9

Best Known (131−93, 131, s)-Nets in Base 9

(131−93, 131, 81)-Net over F₉ — Constructive and digital

Digital (38, 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]

(131−93, 131, 128)-Net over F₉ — Digital

Digital (38, 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]

(131−93, 131, 1091)-Net in Base 9 — Upper bound on s

There is no (38, 131, 1092)-net in base 9, because

1 times m-reduction [i] would yield (38, 130, 1092)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11651 284611 523793 182531 682427 204096 212131 409663 038907 999761 855275 076026 045985 866083 270511 011765 978385 673614 843583 082150 028609 > 9¹³⁰ [i]