MinT - Best Known (41, 41+38, s)-Nets in Base 3

Best Known (41, 41+38, s)-Nets in Base 3

(41, 41+38, 44)-Net over F₃ — Constructive and digital

Digital (41, 79, 44)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (7, 26, 16)-net over F₃, using
  - net from sequence [i] based on digital (7, 15)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 7 and N(F) ≥ 16, using
      - an explicitly constructive algebraic function field [i]
2. digital (15, 53, 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]

(41, 41+38, 56)-Net over F₃ — Digital

Digital (41, 79, 56)-net over F₃, using

t-expansion [i] based on digital (40, 79, 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]

(41, 41+38, 363)-Net in Base 3 — Upper bound on s

There is no (41, 79, 364)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 49 726450 875903 384193 681275 514330 636113 > 3⁷⁹ [i]