MinT - Best Known (142−58, 142, s)-Nets in Base 3

Best Known (142−58, 142, s)-Nets in Base 3

(142−58, 142, 128)-Net over F₃ — Constructive and digital

Digital (84, 142, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 71, 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]

(142−58, 142, 132)-Net over F₃ — Digital

Digital (84, 142, 132)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−58, 142, 1237)-Net in Base 3 — Upper bound on s

There is no (84, 142, 1238)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 57 049050 559147 896786 107588 780458 633997 326113 193617 446341 305236 449749 > 3¹⁴² [i]