MinT - Best Known (193−47, 193, s)-Nets in Base 3

Best Known (193−47, 193, s)-Nets in Base 3

(193−47, 193, 400)-Net over F₃ — Constructive and digital

Digital (146, 193, 400)-net over F₃, using

3¹ times duplication [i] based on digital (145, 192, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 48, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(193−47, 193, 918)-Net over F₃ — Digital

Digital (146, 193, 918)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−47, 193, 45303)-Net in Base 3 — Upper bound on s

There is no (146, 193, 45304)-net in base 3, because

1 times m-reduction [i] would yield (146, 192, 45304)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 485052 091989 846316 438342 886795 330677 932152 683668 022054 879779 137742 319908 848340 972680 861345 > 3¹⁹² [i]