MinT - Best Known (58, 58+37, s)-Nets in Base 3

Best Known (58, 58+37, s)-Nets in Base 3

(58, 58+37, 80)-Net over F₃ — Constructive and digital

Digital (58, 95, 80)-net over F₃, using

5 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+37, 109)-Net over F₃ — Digital

Digital (58, 95, 109)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+37, 1154)-Net in Base 3 — Upper bound on s

There is no (58, 95, 1155)-net in base 3, because

1 times m-reduction [i] would yield (58, 94, 1155)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 716 979847 383774 934970 340929 159882 686046 951557 > 3⁹⁴ [i]