MinT - Best Known (151, 151+53, s)-Nets in Base 2

Best Known (151, 151+53, s)-Nets in Base 2

(151, 151+53, 195)-Net over F₂ — Constructive and digital

Digital (151, 204, 195)-net over F₂, using

t-expansion [i] based on digital (150, 204, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 68, 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]

(151, 151+53, 257)-Net over F₂ — Digital

Digital (151, 204, 257)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+53, 2325)-Net in Base 2 — Upper bound on s

There is no (151, 204, 2326)-net in base 2, because

1 times m-reduction [i] would yield (151, 203, 2326)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12 889810 584179 947061 235331 499885 428982 673823 803489 085810 030400 > 2²⁰³ [i]