MinT - Best Known (58, 58+35, s)-Nets in Base 3

Best Known (58, 58+35, s)-Nets in Base 3

(58, 58+35, 80)-Net over F₃ — Constructive and digital

Digital (58, 93, 80)-net over F₃, using

7 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+35, 119)-Net over F₃ — Digital

Digital (58, 93, 119)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+35, 1354)-Net in Base 3 — Upper bound on s

There is no (58, 93, 1355)-net in base 3, because

1 times m-reduction [i] would yield (58, 92, 1355)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 79 127165 618245 387624 363532 334561 830375 229687 > 3⁹² [i]