MinT - Best Known (12, 12+84, s)-Nets in Base 9

Best Known (12, 12+84, s)-Nets in Base 9

(12, 12+84, 40)-Net over F₉ — Constructive and digital

Digital (12, 96, 40)-net over F₉, using

t-expansion [i] based on digital (8, 96, 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]

(12, 12+84, 56)-Net over F₉ — Digital

Digital (12, 96, 56)-net over F₉, using

net from sequence [i] based on digital (12, 55)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 12 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(12, 12+84, 121)-Net in Base 9 — Upper bound on s

There is no (12, 96, 122)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁹⁶, 122, S₉, 84), but
- the linear programming bound shows that MÂ â‰¥ 7350 464043 164478 762472 775073 177926 775600 208568 194072 146215 007174 838735 287492 367277 662901 948560 686754 817855 005217 285511 / 159 933807 690753 892414 994375 > 9⁹⁶ [i]