MinT - Best Known (156−65, 156, s)-Nets in Base 3

Best Known (156−65, 156, s)-Nets in Base 3

(156−65, 156, 128)-Net over F₃ — Constructive and digital

Digital (91, 156, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 78, 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]

(156−65, 156, 135)-Net over F₃ — Digital

Digital (91, 156, 135)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−65, 156, 1277)-Net in Base 3 — Upper bound on s

There is no (91, 156, 1278)-net in base 3, because

1 times m-reduction [i] would yield (91, 155, 1278)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 90 541506 593612 342193 673095 921794 070923 924989 455199 011680 123112 401073 063745 > 3¹⁵⁵ [i]