MinT - Best Known (248−99, 248, s)-Nets in Base 3

Best Known (248−99, 248, s)-Nets in Base 3

(248−99, 248, 156)-Net over F₃ — Constructive and digital

Digital (149, 248, 156)-net over F₃, using

t-expansion [i] based on digital (147, 248, 156)-net over F₃, using
- 2 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]

(248−99, 248, 227)-Net over F₃ — Digital

Digital (149, 248, 227)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−99, 248, 2380)-Net in Base 3 — Upper bound on s

There is no (149, 248, 2381)-net in base 3, because

1 times m-reduction [i] would yield (149, 247, 2381)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7131 684098 287280 796117 502763 599503 655225 001795 136041 744166 500813 655300 924202 389926 507125 298526 507618 543844 063228 903131 > 3²⁴⁷ [i]