MinT - Best Known (81, 136, s)-Nets in Base 3

Best Known (81, 136, s)-Nets in Base 3

(81, 136, 128)-Net over F₃ — Constructive and digital

Digital (81, 136, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 68, 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]

(81, 136, 131)-Net over F₃ — Digital

Digital (81, 136, 131)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 136, 1301)-Net in Base 3 — Upper bound on s

There is no (81, 136, 1302)-net in base 3, because

1 times m-reduction [i] would yield (81, 135, 1302)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26282 077333 276874 065821 588790 866211 328900 307135 558865 340535 938097 > 3¹³⁵ [i]