MinT - Best Known (37, 37+64, s)-Nets in Base 3

Best Known (37, 37+64, s)-Nets in Base 3

(37, 37+64, 38)-Net over F₃ — Constructive and digital

Digital (37, 101, 38)-net over F₃, using

t-expansion [i] based on digital (32, 101, 38)-net over F₃, using
- net from sequence [i] based on digital (32, 37)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
    - an explicitly constructive algebraic function field [i]

(37, 37+64, 52)-Net over F₃ — Digital

Digital (37, 101, 52)-net over F₃, using

net from sequence [i] based on digital (37, 51)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 37 and N(F) ≥ 52, using
  - a curve from the manYPoints database [i]

(37, 37+64, 126)-Net in Base 3 — Upper bound on s

There is no (37, 101, 127)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰¹, 127, S₃, 64), but
- the linear programming bound shows that MÂ â‰¥ 132692 643818 453126 760955 265992 737829 772140 573200 031364 791351 063599 / 81918 983084 213275 > 3¹⁰¹ [i]