MinT - Best Known (223−52, 223, s)-Nets in Base 3

Best Known (223−52, 223, s)-Nets in Base 3

(223−52, 223, 464)-Net over F₃ — Constructive and digital

Digital (171, 223, 464)-net over F₃, using

t-expansion [i] based on digital (170, 223, 464)-net over F₃, using
- 1 times m-reduction [i] based on digital (170, 224, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 56, 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]

(223−52, 223, 1235)-Net over F₃ — Digital

Digital (171, 223, 1235)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−52, 223, 65211)-Net in Base 3 — Upper bound on s

There is no (171, 223, 65212)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25008 646957 667916 839270 998448 364265 901867 641929 623342 577173 813315 261381 816398 248746 947027 915507 198774 175625 > 3²²³ [i]