MinT - Best Known (210−51, 210, s)-Nets in Base 2

Best Known (210−51, 210, s)-Nets in Base 2

(210−51, 210, 195)-Net over F₂ — Constructive and digital

Digital (159, 210, 195)-net over F₂, using

t-expansion [i] based on digital (158, 210, 195)-net over F₂, using
- 6 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]

(210−51, 210, 315)-Net over F₂ — Digital

Digital (159, 210, 315)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−51, 210, 3306)-Net in Base 2 — Upper bound on s

There is no (159, 210, 3307)-net in base 2, because

1 times m-reduction [i] would yield (159, 209, 3307)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 823 013854 074770 063134 245614 560199 317690 026671 361290 709235 717304 > 2²⁰⁹ [i]