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

Best Known (10, s)-Sequences in Base 9

(10, 39)-Sequence over F₉ — Constructive and digital

Digital (10, 39)-sequence over F₉, using

t-expansion [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, 53)-Sequence over F₉ — Digital

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, 95)-Sequence in Base 9 — Upper bound on s

There is no (10, 96)-sequence in base 9, because

net from sequence [i] would yield (10, m, 97)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (10, 87, 97)-net in base 9, but
  - extracting embedded orthogonal array [i] would yield OA(9⁸⁷, 97, S₉, 77), but
    - the linear programming bound shows that MÂ â‰¥ 577 508372 587460 541806 827932 218426 944109 871880 135970 034666 716258 074835 618754 104688 984869 879637 / 5272 197931 > 9⁸⁷ [i]