MinT - Best Known (125−44, 125, s)-Nets in Base 3

Best Known (125−44, 125, s)-Nets in Base 3

(125−44, 125, 148)-Net over F₃ — Constructive and digital

Digital (81, 125, 148)-net over F₃, using

3 times m-reduction [i] based on digital (81, 128, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 64, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(125−44, 125, 183)-Net over F₃ — Digital

Digital (81, 125, 183)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−44, 125, 2305)-Net in Base 3 — Upper bound on s

There is no (81, 125, 2306)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 439670 314495 658774 284901 382362 872976 542679 166842 359739 856093 > 3¹²⁵ [i]