MinT - Best Known (125−35, 125, s)-Nets in Base 3

Best Known (125−35, 125, s)-Nets in Base 3

(125−35, 125, 228)-Net over F₃ — Constructive and digital

Digital (90, 125, 228)-net over F₃, using

1 times m-reduction [i] based on digital (90, 126, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 42, 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]

(125−35, 125, 382)-Net over F₃ — Digital

Digital (90, 125, 382)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−35, 125, 10825)-Net in Base 3 — Upper bound on s

There is no (90, 125, 10826)-net in base 3, because

1 times m-reduction [i] would yield (90, 124, 10826)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 145758 731981 912171 621523 660228 282568 316509 267779 564111 820533 > 3¹²⁴ [i]