MinT - Best Known (249−42, 249, s)-Nets in Base 2

Best Known (249−42, 249, s)-Nets in Base 2

(249−42, 249, 490)-Net over F₂ — Constructive and digital

Digital (207, 249, 490)-net over F₂, using

1 times m-reduction [i] based on digital (207, 250, 490)-net over F₂, using
- trace code for nets [i] based on digital (7, 50, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(249−42, 249, 1106)-Net over F₂ — Digital

Digital (207, 249, 1106)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−42, 249, 32168)-Net in Base 2 — Upper bound on s

There is no (207, 249, 32169)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 904 951992 386895 403197 893754 941151 325564 689301 949949 913380 027077 978092 014520 > 2²⁴⁹ [i]