MinT - Best Known (46, 46+80, s)-Nets in Base 3

Best Known (46, 46+80, s)-Nets in Base 3

(46, 46+80, 48)-Net over F₃ — Constructive and digital

Digital (46, 126, 48)-net over F₃, using

t-expansion [i] based on digital (45, 126, 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]

(46, 46+80, 56)-Net over F₃ — Digital

Digital (46, 126, 56)-net over F₃, using

t-expansion [i] based on digital (40, 126, 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]

(46, 46+80, 149)-Net in Base 3 — Upper bound on s

There is no (46, 126, 150)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹²⁶, 150, S₃, 80), but
- the linear programming bound shows that MÂ â‰¥ 1 744284 668385 163500 346306 269658 104769 929699 691581 439318 970712 105752 702784 / 1 186440 433087 > 3¹²⁶ [i]