MinT - Best Known (147, 193, s)-Nets in Base 3

Best Known (147, 193, s)-Nets in Base 3

(147, 193, 464)-Net over F₃ — Constructive and digital

Digital (147, 193, 464)-net over F₃, using

3¹ times duplication [i] based on digital (146, 192, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 48, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(147, 193, 1003)-Net over F₃ — Digital

Digital (147, 193, 1003)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 193, 47521)-Net in Base 3 — Upper bound on s

There is no (147, 193, 47522)-net in base 3, because

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]