MinT - Best Known (95−38, 95, s)-Nets in Base 2

Best Known (95−38, 95, s)-Nets in Base 2

(95−38, 95, 44)-Net over F₂ — Constructive and digital

Digital (57, 95, 44)-net over F₂, using

1 times m-reduction [i] based on digital (57, 96, 44)-net over F₂, using
- trace code for nets [i] based on digital (9, 48, 22)-net over F₄, using
  - net from sequence [i] based on digital (9, 21)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
      - an explicitly constructive algebraic function field [i]

(95−38, 95, 52)-Net over F₂ — Digital

Digital (57, 95, 52)-net over F₂, using

1 times m-reduction [i] based on digital (57, 96, 52)-net over F₂, using
- trace code for nets [i] based on digital (9, 48, 26)-net over F₄, using
  - net from sequence [i] based on digital (9, 25)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 26, using
      - Drinfeld modules of rank 1 [i]

(95−38, 95, 227)-Net in Base 2 — Upper bound on s

There is no (57, 95, 228)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 42539 154407 561291 282560 600502 > 2⁹⁵ [i]