MinT - Best Known (251−92, 251, s)-Nets in Base 2

Best Known (251−92, 251, s)-Nets in Base 2

(251−92, 251, 112)-Net over F₂ — Constructive and digital

Digital (159, 251, 112)-net over F₂, using

1 times m-reduction [i] based on digital (159, 252, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 126, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(251−92, 251, 137)-Net over F₂ — Digital

Digital (159, 251, 137)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−92, 251, 724)-Net in Base 2 — Upper bound on s

There is no (159, 251, 725)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3742 424160 505864 348323 486198 722962 541945 837287 526862 448534 812933 383019 600960 > 2²⁵¹ [i]