MinT - Best Known (56−24, 56, s)-Nets in Base 2

Best Known (56−24, 56, s)-Nets in Base 2

(56−24, 56, 30)-Net over F₂ — Constructive and digital

Digital (32, 56, 30)-net over F₂, using

trace code for nets [i] based on digital (4, 28, 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]

(56−24, 56, 31)-Net over F₂ — Digital

Digital (32, 56, 31)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(56−24, 56, 117)-Net in Base 2 — Upper bound on s

There is no (32, 56, 118)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 73431 479596 730022 > 2⁵⁶ [i]