MinT - Best Known (11, s)-Sequences in Base 9

Best Known (11, s)-Sequences in Base 9

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

Digital (11, 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]

(11, 54)-Sequence over F₉ — Digital

Digital (11, 54)-sequence over F₉, using

Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 11 and N(F) ≥ 55, using
- a curve from the manYPoints database [i]

(11, 103)-Sequence in Base 9 — Upper bound on s

There is no (11, 104)-sequence in base 9, because

net from sequence [i] would yield (11, m, 105)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (11, 95, 105)-net in base 9, but
  - extracting embedded orthogonal array [i] would yield OA(9⁹⁵, 105, S₉, 84), but
    - the linear programming bound shows that MÂ â‰¥ 1240 505866 046627 131068 555034 347769 450501 463301 708903 427699 923262 975474 963339 381628 644774 672768 499337 / 265 061875 > 9⁹⁵ [i]