MinT - Best Known (33, 57, s)-Nets in Base 2

Best Known (33, 57, s)-Nets in Base 2

(33, 57, 30)-Net over F₂ — Constructive and digital

Digital (33, 57, 30)-net over F₂, using

1 times m-reduction [i] based on digital (33, 58, 30)-net over F₂, using
- trace code for nets [i] based on digital (4, 29, 15)-net over F₄, using
  - net from sequence [i] based on digital (4, 14)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
      - an explicitly constructive algebraic function field [i]

(33, 57, 32)-Net over F₂ — Digital

Digital (33, 57, 32)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(33, 57, 125)-Net in Base 2 — Upper bound on s

There is no (33, 57, 126)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 147493 246130 096571 > 2⁵⁷ [i]