MinT - Best Known (10, 60, s)-Nets in Base 9

Best Known (10, 60, s)-Nets in Base 9

(10, 60, 40)-Net over F₉ — Constructive and digital

Digital (10, 60, 40)-net over F₉, using

t-expansion [i] based on digital (8, 60, 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, 60, 54)-Net over F₉ — Digital

Digital (10, 60, 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, 60, 210)-Net in Base 9 — Upper bound on s

There is no (10, 60, 211)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶⁰, 211, S₉, 50), but
- the linear programming bound shows that MÂ â‰¥ 362 946351 247877 551197 334295 171587 494630 197117 344940 348073 667909 732517 067413 525879 000428 141424 135226 959515 931878 892113 309260 / 190327 561788 293797 711423 387377 678882 395847 459779 092924 471252 008853 > 9⁶⁰ [i]