MinT - Best Known (187−48, 187, s)-Nets in Base 2

Best Known (187−48, 187, s)-Nets in Base 2

(187−48, 187, 195)-Net over F₂ — Constructive and digital

Digital (139, 187, 195)-net over F₂, using

2¹ times duplication [i] based on digital (138, 186, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 62, 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]

(187−48, 187, 247)-Net over F₂ — Digital

Digital (139, 187, 247)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−48, 187, 2136)-Net in Base 2 — Upper bound on s

There is no (139, 187, 2137)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 196 367292 854657 559881 519998 745389 801206 123271 787890 784117 > 2¹⁸⁷ [i]