MinT - Best Known (154−34, 154, s)-Nets in Base 2

Best Known (154−34, 154, s)-Nets in Base 2

(154−34, 154, 195)-Net over F₂ — Constructive and digital

Digital (120, 154, 195)-net over F₂, using

5 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]

(154−34, 154, 315)-Net over F₂ — Digital

Digital (120, 154, 315)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−34, 154, 3802)-Net in Base 2 — Upper bound on s

There is no (120, 154, 3803)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22872 399063 143220 706484 714564 004058 975287 057124 > 2¹⁵⁴ [i]