MinT - Best Known (194−47, 194, s)-Nets in Base 3

Best Known (194−47, 194, s)-Nets in Base 3

(194−47, 194, 400)-Net over F₃ — Constructive and digital

Digital (147, 194, 400)-net over F₃, using

3² 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]

(194−47, 194, 941)-Net over F₃ — Digital

Digital (147, 194, 941)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−47, 194, 47521)-Net in Base 3 — Upper bound on s

There is no (147, 194, 47522)-net in base 3, because

1 times m-reduction [i] would yield (147, 193, 47522)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 121 478964 207894 182882 354999 076049 372845 301827 886808 825060 189845 245968 758864 902275 222119 950921 > 3¹⁹³ [i]