MinT - Best Known (185−79, 185, s)-Nets in Base 3

Best Known (185−79, 185, s)-Nets in Base 3

(185−79, 185, 128)-Net over F₃ — Constructive and digital

Digital (106, 185, 128)-net over F₃, using

1 times m-reduction [i] based on digital (106, 186, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 93, 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]

(185−79, 185, 145)-Net over F₃ — Digital

Digital (106, 185, 145)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−79, 185, 1334)-Net in Base 3 — Upper bound on s

There is no (106, 185, 1335)-net in base 3, because

1 times m-reduction [i] would yield (106, 184, 1335)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6315 808399 505672 274919 332731 834996 335582 071713 163968 178858 729889 732504 741231 822772 019219 > 3¹⁸⁴ [i]