MinT - Best Known (75−66, 75, s)-Nets in Base 9

Best Known (75−66, 75, s)-Nets in Base 9

(75−66, 75, 40)-Net over F₉ — Constructive and digital

Digital (9, 75, 40)-net over F₉, using

t-expansion [i] based on digital (8, 75, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(75−66, 75, 48)-Net over F₉ — Digital

Digital (9, 75, 48)-net over F₉, using

net from sequence [i] based on digital (9, 47)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 9 and N(F) ≥ 48, using
  - a curve from the manYPoints database [i]

(75−66, 75, 107)-Net in Base 9 — Upper bound on s

There is no (9, 75, 108)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁷⁵, 108, S₉, 66), but
- the linear programming bound shows that MÂ â‰¥ 36 745250 488498 109540 897660 553446 362145 339494 860007 486793 301671 320986 078563 644195 804719 181383 775725 728283 / 91 304677 278818 732326 315853 090120 > 9⁷⁵ [i]