MinT - Best Known (10, 59, s)-Nets in Base 9

Best Known (10, 59, s)-Nets in Base 9

(10, 59, 40)-Net over F₉ — Constructive and digital

Digital (10, 59, 40)-net over F₉, using

t-expansion [i] based on digital (8, 59, 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, 59, 54)-Net over F₉ — Digital

Digital (10, 59, 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, 59, 211)-Net in Base 9 — Upper bound on s

There is no (10, 59, 212)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵⁹, 212, S₉, 49), but
- the linear programming bound shows that MÂ â‰¥ 3 155024 117081 328597 256541 006101 219348 097949 504650 344107 398718 648549 766245 392589 994914 862766 408662 412145 496860 666020 065980 / 15089 211015 526220 334400 399857 026924 402800 402203 910905 987118 214957 > 9⁵⁹ [i]