MinT - Best Known (209−51, 209, s)-Nets in Base 2

Best Known (209−51, 209, s)-Nets in Base 2

(209−51, 209, 195)-Net over F₂ — Constructive and digital

Digital (158, 209, 195)-net over F₂, using

7 times m-reduction [i] based on digital (158, 216, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 72, 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]

(209−51, 209, 310)-Net over F₂ — Digital

Digital (158, 209, 310)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−51, 209, 3215)-Net in Base 2 — Upper bound on s

There is no (158, 209, 3216)-net in base 2, because

1 times m-reduction [i] would yield (158, 208, 3216)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 412 874311 202209 740331 413574 236977 977689 933389 560814 883057 131320 > 2²⁰⁸ [i]