MinT - Best Known (152−63, 152, s)-Nets in Base 3

Best Known (152−63, 152, s)-Nets in Base 3

(152−63, 152, 128)-Net over F₃ — Constructive and digital

Digital (89, 152, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 76, 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]

(152−63, 152, 134)-Net over F₃ — Digital

Digital (89, 152, 134)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−63, 152, 1279)-Net in Base 3 — Upper bound on s

There is no (89, 152, 1280)-net in base 3, because

1 times m-reduction [i] would yield (89, 151, 1280)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 133566 059564 763974 341346 064677 123552 124944 797903 259389 789917 540266 589185 > 3¹⁵¹ [i]