MinT - Best Known (158−37, 158, s)-Nets in Base 2

Best Known (158−37, 158, s)-Nets in Base 2

(158−37, 158, 195)-Net over F₂ — Constructive and digital

Digital (121, 158, 195)-net over F₂, using

t-expansion [i] based on digital (120, 158, 195)-net over F₂, using
- 1 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]

(158−37, 158, 273)-Net over F₂ — Digital

Digital (121, 158, 273)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−37, 158, 3163)-Net in Base 2 — Upper bound on s

There is no (121, 158, 3164)-net in base 2, because

1 times m-reduction [i] would yield (121, 157, 3164)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 183177 567335 282691 214640 940186 654860 046332 464309 > 2¹⁵⁷ [i]