MinT - Best Known (41, 41+35, s)-Nets in Base 3

Best Known (41, 41+35, s)-Nets in Base 3

(41, 41+35, 56)-Net over F₃ — Constructive and digital

Digital (41, 76, 56)-net over F₃, using

trace code for nets [i] based on digital (3, 38, 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]

(41, 41+35, 58)-Net over F₃ — Digital

Digital (41, 76, 58)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(41, 41+35, 440)-Net in Base 3 — Upper bound on s

There is no (41, 76, 441)-net in base 3, because

1 times m-reduction [i] would yield (41, 75, 441)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 615377 890790 642393 603985 507287 076915 > 3⁷⁵ [i]