MinT - Best Known (140−57, 140, s)-Nets in Base 3

Best Known (140−57, 140, s)-Nets in Base 3

(140−57, 140, 128)-Net over F₃ — Constructive and digital

Digital (83, 140, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 70, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(140−57, 140, 131)-Net over F₃ — Digital

Digital (83, 140, 131)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−57, 140, 1292)-Net in Base 3 — Upper bound on s

There is no (83, 140, 1293)-net in base 3, because

1 times m-reduction [i] would yield (83, 139, 1293)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 104721 800169 521451 136174 173395 365504 103296 029384 188695 498743 333425 > 3¹³⁹ [i]