MinT - Best Known (118−74, 118, s)-Nets in Base 3

Best Known (118−74, 118, s)-Nets in Base 3

(118−74, 118, 42)-Net over F₃ — Constructive and digital

Digital (44, 118, 42)-net over F₃, using

t-expansion [i] based on digital (39, 118, 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]

(118−74, 118, 56)-Net over F₃ — Digital

Digital (44, 118, 56)-net over F₃, using

t-expansion [i] based on digital (40, 118, 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]

(118−74, 118, 148)-Net in Base 3 — Upper bound on s

There is no (44, 118, 149)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹¹⁸, 149, S₃, 74), but
- the linear programming bound shows that MÂ â‰¥ 14631 013686 142997 953866 980562 476233 047154 143146 692997 967075 486096 911649 489501 / 62 737137 135696 970925 > 3¹¹⁸ [i]