MinT - Best Known (35, 35+82, s)-Nets in Base 9

Best Known (35, 35+82, s)-Nets in Base 9

(35, 35+82, 81)-Net over F₉ — Constructive and digital

Digital (35, 117, 81)-net over F₉, using

t-expansion [i] based on digital (32, 117, 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]

(35, 35+82, 128)-Net over F₉ — Digital

Digital (35, 117, 128)-net over F₉, using

t-expansion [i] based on digital (33, 117, 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]

(35, 35+82, 1041)-Net in Base 9 — Upper bound on s

There is no (35, 117, 1042)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4531 230909 444654 655177 111138 707590 012707 533044 956895 546568 380457 234000 565901 538456 605621 068416 676185 231509 956113 > 9¹¹⁷ [i]