MinT - Best Known (115−70, 115, s)-Nets in Base 9

Best Known (115−70, 115, s)-Nets in Base 9

(115−70, 115, 81)-Net over F₉ — Constructive and digital

Digital (45, 115, 81)-net over F₉, using

t-expansion [i] based on digital (32, 115, 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]

(115−70, 115, 147)-Net over F₉ — Digital

Digital (45, 115, 147)-net over F₉, using

t-expansion [i] based on digital (43, 115, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(115−70, 115, 2353)-Net in Base 9 — Upper bound on s

There is no (45, 115, 2354)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55 485784 096612 031540 707035 473241 131775 916452 277288 591553 989314 307866 477455 634394 304714 679726 592426 700546 731761 > 9¹¹⁵ [i]