MinT - Best Known (10, 10+47, s)-Nets in Base 9

Best Known (10, 10+47, s)-Nets in Base 9

(10, 10+47, 40)-Net over F₉ — Constructive and digital

Digital (10, 57, 40)-net over F₉, using

t-expansion [i] based on digital (8, 57, 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+47, 54)-Net over F₉ — Digital

Digital (10, 57, 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+47, 217)-Net in Base 9 — Upper bound on s

There is no (10, 57, 218)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵⁷, 218, S₉, 47), but
- the linear programming bound shows that MÂ â‰¥ 1 573504 296730 432926 330868 340153 267954 161130 285390 572978 556571 874352 891760 254841 070774 312892 756750 098731 015600 079498 200964 625625 / 608317 074764 570521 061989 240382 708967 793353 755025 440521 301151 766503 416009 > 9⁵⁷ [i]