MinT - Best Known (15, 15+105, s)-Nets in Base 9

Best Known (15, 15+105, s)-Nets in Base 9

(15, 15+105, 64)-Net over F₉ — Constructive and digital

Digital (15, 120, 64)-net over F₉, using

t-expansion [i] based on digital (13, 120, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(15, 15+105, 136)-Net in Base 9 — Upper bound on s

There is no (15, 120, 137)-net in base 9, because

1 times m-reduction [i] would yield (15, 119, 137)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9¹¹⁹, 137, S₉, 104), but
  - the linear programming bound shows that MÂ â‰¥ 1 649743 959172 993378 210906 967412 042627 075594 345401 873516 549288 005769 316925 057707 239007 022709 124331 368314 618099 062045 429872 721572 150117 / 4 003686 893566 937500 > 9¹¹⁹ [i]