MinT - Best Known (58, 58+49, s)-Nets in Base 3

Best Known (58, 58+49, s)-Nets in Base 3

(58, 58+49, 60)-Net over F₃ — Constructive and digital

Digital (58, 107, 60)-net over F₃, using

1 times m-reduction [i] based on digital (58, 108, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 54, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]

(58, 58+49, 76)-Net over F₃ — Digital

Digital (58, 107, 76)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+49, 604)-Net in Base 3 — Upper bound on s

There is no (58, 107, 605)-net in base 3, because

1 times m-reduction [i] would yield (58, 106, 605)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 384 914968 271972 875296 083364 836520 219155 523950 354721 > 3¹⁰⁶ [i]