MinT - Best Known (14, 40, s)-Nets in Base 3

Best Known (14, 40, s)-Nets in Base 3

(14, 40, 24)-Net over F₃ — Constructive and digital

Digital (14, 40, 24)-net over F₃, using

t-expansion [i] based on digital (13, 40, 24)-net over F₃, using
- net from sequence [i] based on digital (13, 23)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(14, 40, 65)-Net in Base 3 — Upper bound on s

There is no (14, 40, 66)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁴⁰, 66, S₃, 26), but
- the linear programming bound shows that MÂ â‰¥ 1 052217 758394 261366 974482 389978 638457 / 80396 935501 754368 > 3⁴⁰ [i]