MinT - Best Known (252−69, 252, s)-Nets in Base 2

Best Known (252−69, 252, s)-Nets in Base 2

(252−69, 252, 195)-Net over F₂ — Constructive and digital

Digital (183, 252, 195)-net over F₂, using

t-expansion [i] based on digital (182, 252, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 84, 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]

(252−69, 252, 271)-Net over F₂ — Digital

Digital (183, 252, 271)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−69, 252, 2208)-Net in Base 2 — Upper bound on s

There is no (183, 252, 2209)-net in base 2, because

1 times m-reduction [i] would yield (183, 251, 2209)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3655 229503 131490 824315 911445 644390 199815 859598 137349 562580 172414 104337 731380 > 2²⁵¹ [i]