MinT - Best Known (249−100, 249, s)-Nets in Base 3

Best Known (249−100, 249, s)-Nets in Base 3

(249−100, 249, 156)-Net over F₃ — Constructive and digital

Digital (149, 249, 156)-net over F₃, using

t-expansion [i] based on digital (147, 249, 156)-net over F₃, using
- 1 times m-reduction [i] based on digital (147, 250, 156)-net over F₃, using
  - trace code for nets [i] based on digital (22, 125, 78)-net over F₉, using
    - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
        F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(249−100, 249, 224)-Net over F₃ — Digital

Digital (149, 249, 224)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−100, 249, 2266)-Net in Base 3 — Upper bound on s

There is no (149, 249, 2267)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63966 136906 028778 656995 823278 807370 158939 469996 083551 875245 425246 988763 203704 625979 024155 577566 396691 194275 678154 035189 > 3²⁴⁹ [i]