MinT - Best Known (41, 112, s)-Nets in Base 3

Best Known (41, 112, s)-Nets in Base 3

(41, 112, 42)-Net over F₃ — Constructive and digital

Digital (41, 112, 42)-net over F₃, using

t-expansion [i] based on digital (39, 112, 42)-net over F₃, using
- net from sequence [i] based on digital (39, 41)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 39 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(41, 112, 56)-Net over F₃ — Digital

Digital (41, 112, 56)-net over F₃, using

t-expansion [i] based on digital (40, 112, 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]

(41, 112, 138)-Net in Base 3 — Upper bound on s

There is no (41, 112, 139)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹¹², 139, S₃, 71), but
- the linear programming bound shows that MÂ â‰¥ 98 919540 835127 996040 877141 197617 116425 497147 443406 496577 779098 602827 / 243 338250 946153 > 3¹¹² [i]