MinT - Best Known (130−95, 130, s)-Nets in Base 9

Best Known (130−95, 130, s)-Nets in Base 9

(130−95, 130, 81)-Net over F₉ — Constructive and digital

Digital (35, 130, 81)-net over F₉, using

t-expansion [i] based on digital (32, 130, 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]

(130−95, 130, 128)-Net over F₉ — Digital

Digital (35, 130, 128)-net over F₉, using

t-expansion [i] based on digital (33, 130, 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]

(130−95, 130, 926)-Net in Base 9 — Upper bound on s

There is no (35, 130, 927)-net in base 9, because

1 times m-reduction [i] would yield (35, 129, 927)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1276 512809 847137 006029 265594 775082 284188 727325 789891 568690 465029 233066 595352 318496 972047 957565 273529 027080 467392 462782 815625 > 9¹²⁹ [i]