MinT - Best Known (67, 67+24, s)-Nets in Base 3

Best Known (67, 67+24, s)-Nets in Base 3

(67, 67+24, 228)-Net over F₃ — Constructive and digital

Digital (67, 91, 228)-net over F₃, using

3¹ times duplication [i] based on digital (66, 90, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 30, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(67, 67+24, 375)-Net over F₃ — Digital

Digital (67, 91, 375)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+24, 10965)-Net in Base 3 — Upper bound on s

There is no (67, 91, 10966)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26 185564 220148 175171 994270 599518 372355 009113 > 3⁹¹ [i]