MinT - Best Known (85, 85+59, s)-Nets in Base 3

Best Known (85, 85+59, s)-Nets in Base 3

(85, 85+59, 128)-Net over F₃ — Constructive and digital

Digital (85, 144, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 72, 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]

(85, 85+59, 132)-Net over F₃ — Digital

Digital (85, 144, 132)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+59, 1286)-Net in Base 3 — Upper bound on s

There is no (85, 144, 1287)-net in base 3, because

1 times m-reduction [i] would yield (85, 143, 1287)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 171 602636 669274 035377 887135 237850 391465 858461 571510 893348 695105 036055 > 3¹⁴³ [i]