MinT - Best Known (142−107, 142, s)-Nets in Base 9

Best Known (142−107, 142, s)-Nets in Base 9

(142−107, 142, 81)-Net over F₉ — Constructive and digital

Digital (35, 142, 81)-net over F₉, using

t-expansion [i] based on digital (32, 142, 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]

(142−107, 142, 128)-Net over F₉ — Digital

Digital (35, 142, 128)-net over F₉, using

t-expansion [i] based on digital (33, 142, 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]

(142−107, 142, 857)-Net in Base 9 — Upper bound on s

There is no (35, 142, 858)-net in base 9, because

1 times m-reduction [i] would yield (35, 141, 858)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 361 227073 844124 877889 013799 468689 906238 199862 887059 522055 309869 643104 974669 942042 616649 619448 924410 949342 891331 923745 918656 264320 128145 > 9¹⁴¹ [i]