MinT - Best Known (66, 66+24, s)-Nets in Base 3

Best Known (66, 66+24, s)-Nets in Base 3

(66, 66+24, 228)-Net over F₃ — Constructive and digital

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]

(66, 66+24, 358)-Net over F₃ — Digital

Digital (66, 90, 358)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+24, 10005)-Net in Base 3 — Upper bound on s

There is no (66, 90, 10006)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 732373 815358 034657 410550 863942 868329 454169 > 3⁹⁰ [i]