MinT - Best Known (89−23, 89, s)-Nets in Base 3

Best Known (89−23, 89, s)-Nets in Base 3

(89−23, 89, 228)-Net over F₃ — Constructive and digital

Digital (66, 89, 228)-net over F₃, using

1 times m-reduction [i] based on 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]

(89−23, 89, 396)-Net over F₃ — Digital

Digital (66, 89, 396)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−23, 89, 16094)-Net in Base 3 — Upper bound on s

There is no (66, 89, 16095)-net in base 3, because

1 times m-reduction [i] would yield (66, 88, 16095)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 970263 550150 845230 101674 831878 587433 808747 > 3⁸⁸ [i]