MinT - Best Known (58, 58+43, s)-Nets in Base 3

Best Known (58, 58+43, s)-Nets in Base 3

(58, 58+43, 72)-Net over F₃ — Constructive and digital

Digital (58, 101, 72)-net over F₃, using

1 times m-reduction [i] based on digital (58, 102, 72)-net over F₃, using
- trace code for nets [i] based on digital (7, 51, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]

(58, 58+43, 89)-Net over F₃ — Digital

Digital (58, 101, 89)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+43, 791)-Net in Base 3 — Upper bound on s

There is no (58, 101, 792)-net in base 3, because

1 times m-reduction [i] would yield (58, 100, 792)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 521410 521120 735204 160614 340694 528236 624806 893745 > 3¹⁰⁰ [i]