MinT - Best Known (120−76, 120, s)-Nets in Base 3

Best Known (120−76, 120, s)-Nets in Base 3

(120−76, 120, 42)-Net over F₃ — Constructive and digital

Digital (44, 120, 42)-net over F₃, using

t-expansion [i] based on digital (39, 120, 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]

(120−76, 120, 56)-Net over F₃ — Digital

Digital (44, 120, 56)-net over F₃, using

t-expansion [i] based on digital (40, 120, 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]

(120−76, 120, 146)-Net in Base 3 — Upper bound on s

There is no (44, 120, 147)-net in base 3, because

1 times m-reduction [i] would yield (44, 119, 147)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3¹¹⁹, 147, S₃, 75), but
  - the linear programming bound shows that MÂ â‰¥ 16 137915 552723 745131 682214 391750 091116 522557 190679 736158 328855 711764 240731 / 23372 130007 496452 > 3¹¹⁹ [i]