MinT - Best Known (67−21, 67, s)-Nets in Base 3

Best Known (67−21, 67, s)-Nets in Base 3

(67−21, 67, 114)-Net over F₃ — Constructive and digital

Digital (46, 67, 114)-net over F₃, using

3¹ times duplication [i] based on digital (45, 66, 114)-net over F₃, using
- trace code for nets [i] based on digital (1, 22, 38)-net over F₂₇, using
  - net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(67−21, 67, 166)-Net over F₃ — Digital

Digital (46, 67, 166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(67−21, 67, 3181)-Net in Base 3 — Upper bound on s

There is no (46, 67, 3182)-net in base 3, because

1 times m-reduction [i] would yield (46, 66, 3182)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30 936365 226436 948886 455859 190701 > 3⁶⁶ [i]