MinT - Best Known (59, 59+35, s)-Nets in Base 3

Best Known (59, 59+35, s)-Nets in Base 3

(59, 59+35, 80)-Net over F₃ — Constructive and digital

Digital (59, 94, 80)-net over F₃, using

8 times m-reduction [i] based on digital (59, 102, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 51, 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]

(59, 59+35, 124)-Net over F₃ — Digital

Digital (59, 94, 124)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+35, 1445)-Net in Base 3 — Upper bound on s

There is no (59, 94, 1446)-net in base 3, because

1 times m-reduction [i] would yield (59, 93, 1446)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 235 874032 744950 850140 153081 854895 065776 176429 > 3⁹³ [i]