MinT - Best Known (159, 159+49, s)-Nets in Base 2

Best Known (159, 159+49, s)-Nets in Base 2

(159, 159+49, 195)-Net over F₂ — Constructive and digital

Digital (159, 208, 195)-net over F₂, using

t-expansion [i] based on digital (158, 208, 195)-net over F₂, using
- 8 times m-reduction [i] based on digital (158, 216, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 72, 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]

(159, 159+49, 338)-Net over F₂ — Digital

Digital (159, 208, 338)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 159+49, 3834)-Net in Base 2 — Upper bound on s

There is no (159, 208, 3835)-net in base 2, because

1 times m-reduction [i] would yield (159, 207, 3835)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 205 733712 407385 994097 556648 740612 829716 961458 631049 846697 541043 > 2²⁰⁷ [i]