MinT - Best Known (47, 47+29, s)-Nets in Base 3

Best Known (47, 47+29, s)-Nets in Base 3

(47, 47+29, 80)-Net over F₃ — Constructive and digital

Digital (47, 76, 80)-net over F₃, using

2 times m-reduction [i] based on digital (47, 78, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 39, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(47, 47+29, 99)-Net over F₃ — Digital

Digital (47, 76, 99)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+29, 1074)-Net in Base 3 — Upper bound on s

There is no (47, 76, 1075)-net in base 3, because

1 times m-reduction [i] would yield (47, 75, 1075)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 615488 913760 982080 094447 624509 360941 > 3⁷⁵ [i]