MinT - Best Known (10, 52, s)-Nets in Base 9

Best Known (10, 52, s)-Nets in Base 9

(10, 52, 40)-Net over F₉ — Constructive and digital

Digital (10, 52, 40)-net over F₉, using

t-expansion [i] based on digital (8, 52, 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, 52, 54)-Net over F₉ — Digital

Digital (10, 52, 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, 52, 230)-Net in Base 9 — Upper bound on s

There is no (10, 52, 231)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵², 231, S₉, 42), but
- the linear programming bound shows that MÂ â‰¥ 62806 428323 479282 469055 115686 775744 496599 261353 418885 536015 092010 531568 711801 949208 817531 523484 302517 028125 / 1441 597602 228910 556315 530534 630769 835138 119124 403200 774509 > 9⁵² [i]