MinT - Best Known (75, 75+29, s)-Nets in Base 3

Best Known (75, 75+29, s)-Nets in Base 3

(75, 75+29, 204)-Net over F₃ — Constructive and digital

Digital (75, 104, 204)-net over F₃, using

1 times m-reduction [i] based on digital (75, 105, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 35, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(75, 75+29, 339)-Net over F₃ — Digital

Digital (75, 104, 339)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+29, 9774)-Net in Base 3 — Upper bound on s

There is no (75, 104, 9775)-net in base 3, because

1 times m-reduction [i] would yield (75, 103, 9775)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 932619 492971 206260 046736 943965 689395 109690 474181 > 3¹⁰³ [i]