MinT - Best Known (38, 38+34, s)-Nets in Base 3

Best Known (38, 38+34, s)-Nets in Base 3

(38, 38+34, 42)-Net over F₃ — Constructive and digital

Digital (38, 72, 42)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (6, 23, 14)-net over F₃, using
  - net from sequence [i] based on digital (6, 13)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 6 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]
2. digital (15, 49, 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]

(38, 38+34, 52)-Net over F₃ — Digital

Digital (38, 72, 52)-net over F₃, using

t-expansion [i] based on digital (37, 72, 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]

(38, 38+34, 360)-Net in Base 3 — Upper bound on s

There is no (38, 72, 361)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 23348 095072 369960 758150 345053 782419 > 3⁷² [i]