MinT - Best Known (217−53, 217, s)-Nets in Base 2

Best Known (217−53, 217, s)-Nets in Base 2

(217−53, 217, 195)-Net over F₂ — Constructive and digital

Digital (164, 217, 195)-net over F₂, using

8 times m-reduction [i] based on digital (164, 225, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 75, 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]

(217−53, 217, 319)-Net over F₂ — Digital

Digital (164, 217, 319)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−53, 217, 3304)-Net in Base 2 — Upper bound on s

There is no (164, 217, 3305)-net in base 2, because

1 times m-reduction [i] would yield (164, 216, 3305)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 105422 941079 552885 378730 130755 913023 358179 912812 319541 993172 641384 > 2²¹⁶ [i]