MinT - Best Known (46, 46+82, s)-Nets in Base 3

Best Known (46, 46+82, s)-Nets in Base 3

(46, 46+82, 48)-Net over F₃ — Constructive and digital

Digital (46, 128, 48)-net over F₃, using

t-expansion [i] based on digital (45, 128, 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+82, 56)-Net over F₃ — Digital

Digital (46, 128, 56)-net over F₃, using

t-expansion [i] based on digital (40, 128, 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+82, 148)-Net in Base 3 — Upper bound on s

There is no (46, 128, 149)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹²⁸, 149, S₃, 82), but
- the linear programming bound shows that MÂ â‰¥ 33 761969 841965 313899 084622 936677 465357 394104 583425 843880 075496 568722 581771 / 1 948280 920300 > 3¹²⁸ [i]