MinT - Best Known (153−37, 153, s)-Nets in Base 2

Best Known (153−37, 153, s)-Nets in Base 2

(153−37, 153, 195)-Net over F₂ — Constructive and digital

Digital (116, 153, 195)-net over F₂, using

trace code for nets [i] based on digital (14, 51, 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]

(153−37, 153, 245)-Net over F₂ — Digital

Digital (116, 153, 245)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−37, 153, 2604)-Net in Base 2 — Upper bound on s

There is no (116, 153, 2605)-net in base 2, because

1 times m-reduction [i] would yield (116, 152, 2605)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5714 275062 511290 052400 375806 960912 993368 915788 > 2¹⁵² [i]