MinT - Best Known (37, 37+36, s)-Nets in Base 3

Best Known (37, 37+36, s)-Nets in Base 3

(37, 37+36, 40)-Net over F₃ — Constructive and digital

Digital (37, 73, 40)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (4, 22, 12)-net over F₃, using
  - net from sequence [i] based on digital (4, 11)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
2. digital (15, 51, 28)-net over F₃, using
  - net from sequence [i] based on digital (15, 27)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]

(37, 37+36, 52)-Net over F₃ — Digital

Digital (37, 73, 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+36, 308)-Net in Base 3 — Upper bound on s

There is no (37, 73, 309)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 71275 583221 988540 426429 301402 940785 > 3⁷³ [i]