MinT - Best Known (212−52, 212, s)-Nets in Base 2

Best Known (212−52, 212, s)-Nets in Base 2

(212−52, 212, 195)-Net over F₂ — Constructive and digital

Digital (160, 212, 195)-net over F₂, using

7 times m-reduction [i] based on digital (160, 219, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 73, 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]

(212−52, 212, 309)-Net over F₂ — Digital

Digital (160, 212, 309)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−52, 212, 2966)-Net in Base 2 — Upper bound on s

There is no (160, 212, 2967)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6597 427739 764961 721498 803449 109662 316716 096034 189336 453514 086480 > 2²¹² [i]