MinT - Best Known (40, 40+34, s)-Nets in Base 3

Best Known (40, 40+34, s)-Nets in Base 3

(40, 40+34, 56)-Net over F₃ — Constructive and digital

Digital (40, 74, 56)-net over F₃, using

trace code for nets [i] based on digital (3, 37, 28)-net over F₉, using
- net from sequence [i] based on digital (3, 27)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
    - the Hermitian function field over F₉ [i]

(40, 40+34, 57)-Net over F₃ — Digital

Digital (40, 74, 57)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+34, 412)-Net in Base 3 — Upper bound on s

There is no (40, 74, 413)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 210058 610992 754767 120230 426961 405947 > 3⁷⁴ [i]