MinT - Best Known (131−85, 131, s)-Nets in Base 3

Best Known (131−85, 131, s)-Nets in Base 3

(131−85, 131, 48)-Net over F₃ — Constructive and digital

Digital (46, 131, 48)-net over F₃, using

t-expansion [i] based on digital (45, 131, 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]

(131−85, 131, 56)-Net over F₃ — Digital

Digital (46, 131, 56)-net over F₃, using

t-expansion [i] based on digital (40, 131, 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]

(131−85, 131, 146)-Net in Base 3 — Upper bound on s

There is no (46, 131, 147)-net in base 3, because

1 times m-reduction [i] would yield (46, 130, 147)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3¹³⁰, 147, S₃, 84), but
  - the linear programming bound shows that MÂ â‰¥ 610951 874237 245179 799757 396293 504258 972145 948730 720728 290459 967541 402306 / 4917 657235 > 3¹³⁰ [i]