MinT - Best Known (226−56, 226, s)-Nets in Base 3

Best Known (226−56, 226, s)-Nets in Base 3

(226−56, 226, 328)-Net over F₃ — Constructive and digital

Digital (170, 226, 328)-net over F₃, using

3² times duplication [i] based on digital (168, 224, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 56, 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]

(226−56, 226, 973)-Net over F₃ — Digital

Digital (170, 226, 973)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−56, 226, 40061)-Net in Base 3 — Upper bound on s

There is no (170, 226, 40062)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 675389 924570 883474 067484 108984 031348 352057 507944 377806 635150 492456 090172 448116 100652 151079 703933 163195 008377 > 3²²⁶ [i]