MinT - Best Known (204−50, 204, s)-Nets in Base 2

Best Known (204−50, 204, s)-Nets in Base 2

(204−50, 204, 195)-Net over F₂ — Constructive and digital

Digital (154, 204, 195)-net over F₂, using

6 times m-reduction [i] based on digital (154, 210, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 70, 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]

(204−50, 204, 300)-Net over F₂ — Digital

Digital (154, 204, 300)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−50, 204, 2874)-Net in Base 2 — Upper bound on s

There is no (154, 204, 2875)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25 902576 767840 346860 125767 833439 268025 090584 417458 751348 005116 > 2²⁰⁴ [i]