MinT - Best Known (157−38, 157, s)-Nets in Base 2

Best Known (157−38, 157, s)-Nets in Base 2

(157−38, 157, 195)-Net over F₂ — Constructive and digital

Digital (119, 157, 195)-net over F₂, using

2¹ times duplication [i] based on digital (118, 156, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 52, 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]

(157−38, 157, 250)-Net over F₂ — Digital

Digital (119, 157, 250)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−38, 157, 2408)-Net in Base 2 — Upper bound on s

There is no (119, 157, 2409)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 183936 387384 142063 145649 030992 345030 361742 239280 > 2¹⁵⁷ [i]