MinT - Best Known (37, 37+67, s)-Nets in Base 3

Best Known (37, 37+67, s)-Nets in Base 3

(37, 37+67, 38)-Net over F₃ — Constructive and digital

Digital (37, 104, 38)-net over F₃, using

t-expansion [i] based on digital (32, 104, 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+67, 52)-Net over F₃ — Digital

Digital (37, 104, 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+67, 122)-Net in Base 3 — Upper bound on s

There is no (37, 104, 123)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰⁴, 123, S₃, 67), but
- the linear programming bound shows that MÂ â‰¥ 103 294511 077294 150845 150900 898012 976547 994331 584148 046100 056813 / 2 419516 539440 > 3¹⁰⁴ [i]