MinT - Best Known (254−73, 254, s)-Nets in Base 2

Best Known (254−73, 254, s)-Nets in Base 2

(254−73, 254, 144)-Net over F₂ — Constructive and digital

Digital (181, 254, 144)-net over F₂, using

1 times m-reduction [i] based on digital (181, 255, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 85, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(254−73, 254, 243)-Net over F₂ — Digital

Digital (181, 254, 243)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−73, 254, 1810)-Net in Base 2 — Upper bound on s

There is no (181, 254, 1811)-net in base 2, because

1 times m-reduction [i] would yield (181, 253, 1811)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14584 737227 458326 210184 292443 052857 998854 182451 161493 911089 627605 792954 825184 > 2²⁵³ [i]