MinT - Best Known (150−115, 150, s)-Nets in Base 9

Best Known (150−115, 150, s)-Nets in Base 9

(150−115, 150, 81)-Net over F₉ — Constructive and digital

Digital (35, 150, 81)-net over F₉, using

t-expansion [i] based on digital (32, 150, 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]

(150−115, 150, 128)-Net over F₉ — Digital

Digital (35, 150, 128)-net over F₉, using

t-expansion [i] based on digital (33, 150, 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]

(150−115, 150, 826)-Net in Base 9 — Upper bound on s

There is no (35, 150, 827)-net in base 9, because

1 times m-reduction [i] would yield (35, 149, 827)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15278 835516 369102 081774 406724 654691 989289 913449 724670 243516 371587 397983 691636 652264 948086 632814 256101 164370 528123 817717 934584 668403 012125 894425 > 9¹⁴⁹ [i]