MinT - Best Known (134−87, 134, s)-Nets in Base 3

Best Known (134−87, 134, s)-Nets in Base 3

(134−87, 134, 48)-Net over F₃ — Constructive and digital

Digital (47, 134, 48)-net over F₃, using

t-expansion [i] based on digital (45, 134, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(134−87, 134, 56)-Net over F₃ — Digital

Digital (47, 134, 56)-net over F₃, using

t-expansion [i] based on digital (40, 134, 56)-net over F₃, using
- net from sequence [i] based on digital (40, 55)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 40 and N(F) ≥ 56, using
    - a curve from the manYPoints database [i]

(134−87, 134, 149)-Net in Base 3 — Upper bound on s

There is no (47, 134, 150)-net in base 3, because

1 times m-reduction [i] would yield (47, 133, 150)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3¹³³, 150, S₃, 86), but
  - the linear programming bound shows that MÂ â‰¥ 10206 967808 467913 747808 389212 583004 511164 705253 854573 732746 285224 754829 / 2 832691 > 3¹³³ [i]