MinT - Best Known (250−59, 250, s)-Nets in Base 3

Best Known (250−59, 250, s)-Nets in Base 3

(250−59, 250, 464)-Net over F₃ — Constructive and digital

Digital (191, 250, 464)-net over F₃, using

3² times duplication [i] based on digital (189, 248, 464)-net over F₃, using
- t-expansion [i] based on digital (188, 248, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 62, 116)-net over F₈₁, using
    - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]

(250−59, 250, 1290)-Net over F₃ — Digital

Digital (191, 250, 1290)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−59, 250, 72875)-Net in Base 3 — Upper bound on s

There is no (191, 250, 72876)-net in base 3, because

1 times m-reduction [i] would yield (191, 249, 72876)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63563 234348 567324 395462 630664 511566 281944 261717 789071 755254 019386 634047 225668 536326 213859 933832 969304 071019 129801 696313 > 3²⁴⁹ [i]