MinT - Best Known (86, 86+56, s)-Nets in Base 3

Best Known (86, 86+56, s)-Nets in Base 3

(86, 86+56, 128)-Net over F₃ — Constructive and digital

Digital (86, 142, 128)-net over F₃, using

4 times m-reduction [i] based on digital (86, 146, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 73, 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]

(86, 86+56, 146)-Net over F₃ — Digital

Digital (86, 142, 146)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+56, 1457)-Net in Base 3 — Upper bound on s

There is no (86, 142, 1458)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 938882 949908 463034 778544 492278 296737 580316 940274 648745 328933 793049 > 3¹⁴² [i]