MinT - Best Known (143−119, 143, s)-Nets in Base 9

Best Known (143−119, 143, s)-Nets in Base 9

(143−119, 143, 78)-Net over F₉ — Constructive and digital

Digital (24, 143, 78)-net over F₉, using

t-expansion [i] based on digital (22, 143, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(143−119, 143, 92)-Net over F₉ — Digital

Digital (24, 143, 92)-net over F₉, using

t-expansion [i] based on digital (23, 143, 92)-net over F₉, using
- net from sequence [i] based on digital (23, 91)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 23 and N(F) ≥ 92, using
    - Drinfeld modules of rank 1 [i]

(143−119, 143, 529)-Net in Base 9 — Upper bound on s

There is no (24, 143, 530)-net in base 9, because

1 times m-reduction [i] would yield (24, 142, 530)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3494 093296 033285 237592 703604 010366 517056 602804 809409 309819 333355 464670 405888 501248 564152 659472 582541 154691 715011 426898 473525 013120 348785 > 9¹⁴² [i]