MinT - Best Known (10, 10+69, s)-Nets in Base 9

Best Known (10, 10+69, s)-Nets in Base 9

(10, 10+69, 40)-Net over F₉ — Constructive and digital

Digital (10, 79, 40)-net over F₉, using

t-expansion [i] based on digital (8, 79, 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]

(10, 10+69, 54)-Net over F₉ — Digital

Digital (10, 79, 54)-net over F₉, using

net from sequence [i] based on digital (10, 53)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 10 and N(F) ≥ 54, using
  - a curve from the manYPoints database [i]

(10, 10+69, 131)-Net in Base 9 — Upper bound on s

There is no (10, 79, 132)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁷⁹, 132, S₉, 69), but
- the linear programming bound shows that MÂ â‰¥ 82143 456841 733045 025037 184834 339788 759237 480264 144856 246919 866218 654116 617519 714028 022580 097394 537401 935596 883951 489551 328402 875986 433398 675003 / 32 504852 932280 461188 690031 134067 093241 319074 039843 373035 929762 817261 > 9⁷⁹ [i]