MinT - Best Known (212−55, 212, s)-Nets in Base 2

Best Known (212−55, 212, s)-Nets in Base 2

(212−55, 212, 195)-Net over F₂ — Constructive and digital

Digital (157, 212, 195)-net over F₂, using

t-expansion [i] based on digital (156, 212, 195)-net over F₂, using
- 1 times m-reduction [i] based on digital (156, 213, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 71, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(212−55, 212, 267)-Net over F₂ — Digital

Digital (157, 212, 267)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−55, 212, 2420)-Net in Base 2 — Upper bound on s

There is no (157, 212, 2421)-net in base 2, because

1 times m-reduction [i] would yield (157, 211, 2421)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3323 733952 507792 164487 701262 024368 642216 615711 736889 932545 809152 > 2²¹¹ [i]