MinT - Best Known (53−43, 53, s)-Nets in Base 9

Best Known (53−43, 53, s)-Nets in Base 9

(53−43, 53, 40)-Net over F₉ — Constructive and digital

Digital (10, 53, 40)-net over F₉, using

t-expansion [i] based on digital (8, 53, 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]

(53−43, 53, 54)-Net over F₉ — Digital

Digital (10, 53, 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]

(53−43, 53, 229)-Net in Base 9 — Upper bound on s

There is no (10, 53, 230)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵³, 230, S₉, 43), but
- the linear programming bound shows that MÂ â‰¥ 382508 330768 262681 424531 939060 949894 362645 150986 481993 500108 490378 926727 449400 712402 405296 718411 458116 515625 / 932 610569 396800 634531 905281 145814 437767 253533 601749 843649 > 9⁵³ [i]