MinT - Best Known (185−46, 185, s)-Nets in Base 3

Best Known (185−46, 185, s)-Nets in Base 3

(185−46, 185, 328)-Net over F₃ — Constructive and digital

Digital (139, 185, 328)-net over F₃, using

3¹ times duplication [i] based on digital (138, 184, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 46, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(185−46, 185, 815)-Net over F₃ — Digital

Digital (139, 185, 815)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−46, 185, 32421)-Net in Base 3 — Upper bound on s

There is no (139, 185, 32422)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18511 364546 633142 148194 615348 926106 267164 788009 556409 991639 562393 530039 748673 800921 824761 > 3¹⁸⁵ [i]