MinT - Best Known (228−57, 228, s)-Nets in Base 3

Best Known (228−57, 228, s)-Nets in Base 3

(228−57, 228, 328)-Net over F₃ — Constructive and digital

Digital (171, 228, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 57, 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]

(228−57, 228, 947)-Net over F₃ — Digital

Digital (171, 228, 947)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−57, 228, 41665)-Net in Base 3 — Upper bound on s

There is no (171, 228, 41666)-net in base 3, because

1 times m-reduction [i] would yield (171, 227, 41666)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 025866 184588 164875 976690 161571 109410 980771 211976 000618 984573 491222 942065 194702 394739 066444 064226 250857 896985 > 3²²⁷ [i]