MinT - Best Known (81, 124, s)-Nets in Base 3

Best Known (81, 124, s)-Nets in Base 3

(81, 124, 148)-Net over F₃ — Constructive and digital

Digital (81, 124, 148)-net over F₃, using

4 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]

(81, 124, 190)-Net over F₃ — Digital

Digital (81, 124, 190)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 124, 2683)-Net in Base 3 — Upper bound on s

There is no (81, 124, 2684)-net in base 3, because

1 times m-reduction [i] would yield (81, 123, 2684)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 48628 890228 409144 510231 696912 292337 465105 389465 729931 620313 > 3¹²³ [i]