MinT - Best Known (125−33, 125, s)-Nets in Base 3

Best Known (125−33, 125, s)-Nets in Base 3

(125−33, 125, 252)-Net over F₃ — Constructive and digital

Digital (92, 125, 252)-net over F₃, using

1 times m-reduction [i] based on digital (92, 126, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 42, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(125−33, 125, 477)-Net over F₃ — Digital

Digital (92, 125, 477)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−33, 125, 16935)-Net in Base 3 — Upper bound on s

There is no (92, 125, 16936)-net in base 3, because

1 times m-reduction [i] would yield (92, 124, 16936)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 145608 942712 750153 402764 982977 920965 223533 060732 560771 894273 > 3¹²⁴ [i]