MinT - Best Known (178−53, 178, s)-Nets in Base 3

Best Known (178−53, 178, s)-Nets in Base 3

(178−53, 178, 228)-Net over F₃ — Constructive and digital

Digital (125, 178, 228)-net over F₃, using

3¹ times duplication [i] based on digital (124, 177, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 59, 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]

(178−53, 178, 411)-Net over F₃ — Digital

Digital (125, 178, 411)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−53, 178, 9314)-Net in Base 3 — Upper bound on s

There is no (125, 178, 9315)-net in base 3, because

1 times m-reduction [i] would yield (125, 177, 9315)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 823247 622171 739123 987758 849245 201996 122853 418103 031686 513571 957059 370491 095637 195637 > 3¹⁷⁷ [i]