MinT - Best Known (146, 146+47, s)-Nets in Base 2

Best Known (146, 146+47, s)-Nets in Base 2

(146, 146+47, 195)-Net over F₂ — Constructive and digital

Digital (146, 193, 195)-net over F₂, using

5 times m-reduction [i] based on digital (146, 198, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 66, 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]

(146, 146+47, 292)-Net over F₂ — Digital

Digital (146, 193, 292)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+47, 3038)-Net in Base 2 — Upper bound on s

There is no (146, 193, 3039)-net in base 2, because

1 times m-reduction [i] would yield (146, 192, 3039)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6322 510109 017445 499484 781249 269801 219844 591209 199229 132102 > 2¹⁹² [i]