MinT - Best Known (157−37, 157, s)-Nets in Base 2

Best Known (157−37, 157, s)-Nets in Base 2

(157−37, 157, 195)-Net over F₂ — Constructive and digital

Digital (120, 157, 195)-net over F₂, using

2 times m-reduction [i] based on digital (120, 159, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 53, 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]

(157−37, 157, 267)-Net over F₂ — Digital

Digital (120, 157, 267)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−37, 157, 3043)-Net in Base 2 — Upper bound on s

There is no (120, 157, 3044)-net in base 2, because

1 times m-reduction [i] would yield (120, 156, 3044)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 91866 934867 433704 092191 296010 474938 411011 744814 > 2¹⁵⁶ [i]