MinT - Best Known (209−53, 209, s)-Nets in Base 2

Best Known (209−53, 209, s)-Nets in Base 2

(209−53, 209, 195)-Net over F₂ — Constructive and digital

Digital (156, 209, 195)-net over F₂, using

4 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]

(209−53, 209, 280)-Net over F₂ — Digital

Digital (156, 209, 280)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−53, 209, 2662)-Net in Base 2 — Upper bound on s

There is no (156, 209, 2663)-net in base 2, because

1 times m-reduction [i] would yield (156, 208, 2663)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 412 163671 786341 030579 592764 454534 537456 111494 175754 009330 964772 > 2²⁰⁸ [i]