MinT - Best Known (75, 75+28, s)-Nets in Base 3

Best Known (75, 75+28, s)-Nets in Base 3

(75, 75+28, 228)-Net over F₃ — Constructive and digital

Digital (75, 103, 228)-net over F₃, using

3¹ times duplication [i] based on digital (74, 102, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 34, 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]

(75, 75+28, 371)-Net over F₃ — Digital

Digital (75, 103, 371)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+28, 9774)-Net in Base 3 — Upper bound on s

There is no (75, 103, 9775)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 932619 492971 206260 046736 943965 689395 109690 474181 > 3¹⁰³ [i]