MinT - Best Known (248−57, 248, s)-Nets in Base 3

Best Known (248−57, 248, s)-Nets in Base 3

(248−57, 248, 640)-Net over F₃ — Constructive and digital

Digital (191, 248, 640)-net over F₃, using

trace code for nets [i] based on digital (5, 62, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(248−57, 248, 1433)-Net over F₃ — Digital

Digital (191, 248, 1433)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−57, 248, 91355)-Net in Base 3 — Upper bound on s

There is no (191, 248, 91356)-net in base 3, because

1 times m-reduction [i] would yield (191, 247, 91356)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7063 121028 995147 143773 988923 115089 779968 446884 037120 941589 185450 356732 974312 102864 744811 833804 419760 356404 283252 438977 > 3²⁴⁷ [i]