MinT - Best Known (82−28, 82, s)-Nets in Base 3

Best Known (82−28, 82, s)-Nets in Base 3

(82−28, 82, 128)-Net over F₃ — Constructive and digital

Digital (54, 82, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 41, 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]

(82−28, 82, 144)-Net over F₃ — Digital

Digital (54, 82, 144)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−28, 82, 1870)-Net in Base 3 — Upper bound on s

There is no (54, 82, 1871)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1338 527511 867597 301797 884591 557709 479941 > 3⁸² [i]