MinT - Best Known (11, 88, s)-Nets in Base 9

Best Known (11, 88, s)-Nets in Base 9

(11, 88, 40)-Net over F₉ — Constructive and digital

Digital (11, 88, 40)-net over F₉, using

t-expansion [i] based on digital (8, 88, 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]

(11, 88, 55)-Net over F₉ — Digital

Digital (11, 88, 55)-net over F₉, using

net from sequence [i] based on 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, 88, 122)-Net in Base 9 — Upper bound on s

There is no (11, 88, 123)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁸⁸, 123, S₉, 77), but
- the linear programming bound shows that MÂ â‰¥ 2 049323 468512 882830 437557 927950 056920 142469 698273 594095 595567 827648 758202 877798 851897 716145 436924 631480 966385 983365 392593 / 2 167432 449328 767824 143653 829858 790048 > 9⁸⁸ [i]