MinT - Best Known (36, 36+74, s)-Nets in Base 9

Best Known (36, 36+74, s)-Nets in Base 9

(36, 36+74, 81)-Net over F₉ — Constructive and digital

Digital (36, 110, 81)-net over F₉, using

t-expansion [i] based on digital (32, 110, 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]

(36, 36+74, 128)-Net over F₉ — Digital

Digital (36, 110, 128)-net over F₉, using

t-expansion [i] based on digital (33, 110, 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]

(36, 36+74, 1235)-Net in Base 9 — Upper bound on s

There is no (36, 110, 1236)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 933 770521 316062 218149 677736 364919 914767 260885 301286 563063 944914 014573 604269 449290 486661 500561 871694 830113 > 9¹¹⁰ [i]