MinT - Best Known (70, 70+26, s)-Nets in Base 3

Best Known (70, 70+26, s)-Nets in Base 3

(70, 70+26, 228)-Net over F₃ — Constructive and digital

Digital (70, 96, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 32, 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]

(70, 70+26, 358)-Net over F₃ — Digital

Digital (70, 96, 358)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+26, 9444)-Net in Base 3 — Upper bound on s

There is no (70, 96, 9445)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6370 859760 333392 507582 163000 026627 953134 802107 > 3⁹⁶ [i]