MinT - Best Known (58, 58+39, s)-Nets in Base 3

Best Known (58, 58+39, s)-Nets in Base 3

(58, 58+39, 80)-Net over F₃ — Constructive and digital

Digital (58, 97, 80)-net over F₃, using

3 times m-reduction [i] based on digital (58, 100, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 50, 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]

(58, 58+39, 101)-Net over F₃ — Digital

Digital (58, 97, 101)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+39, 1002)-Net in Base 3 — Upper bound on s

There is no (58, 97, 1003)-net in base 3, because

1 times m-reduction [i] would yield (58, 96, 1003)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6439 948239 335219 985032 657409 509367 043536 087723 > 3⁹⁶ [i]