MinT - Best Known (150, 150+49, s)-Nets in Base 2

Best Known (150, 150+49, s)-Nets in Base 2

(150, 150+49, 195)-Net over F₂ — Constructive and digital

Digital (150, 199, 195)-net over F₂, using

5 times m-reduction [i] based on digital (150, 204, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 68, 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]

(150, 150+49, 291)-Net over F₂ — Digital

Digital (150, 199, 291)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+49, 2949)-Net in Base 2 — Upper bound on s

There is no (150, 199, 2950)-net in base 2, because

1 times m-reduction [i] would yield (150, 198, 2950)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 404608 736963 670353 412737 113785 001995 124370 658120 883040 627536 > 2¹⁹⁸ [i]