MinT - Best Known (214−53, 214, s)-Nets in Base 3

Best Known (214−53, 214, s)-Nets in Base 3

(214−53, 214, 328)-Net over F₃ — Constructive and digital

Digital (161, 214, 328)-net over F₃, using

3² times duplication [i] based on digital (159, 212, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 53, 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]

(214−53, 214, 932)-Net over F₃ — Digital

Digital (161, 214, 932)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−53, 214, 42729)-Net in Base 3 — Upper bound on s

There is no (161, 214, 42730)-net in base 3, because

1 times m-reduction [i] would yield (161, 213, 42730)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 423595 084328 982722 952599 710583 302366 380278 690652 475694 033773 464401 621628 528054 929929 580138 976282 565941 > 3²¹³ [i]