MinT - Best Known (197−49, 197, s)-Nets in Base 2

Best Known (197−49, 197, s)-Nets in Base 2

(197−49, 197, 195)-Net over F₂ — Constructive and digital

Digital (148, 197, 195)-net over F₂, using

4 times m-reduction [i] based on digital (148, 201, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 67, 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]

(197−49, 197, 280)-Net over F₂ — Digital

Digital (148, 197, 280)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−49, 197, 2781)-Net in Base 2 — Upper bound on s

There is no (148, 197, 2782)-net in base 2, because

1 times m-reduction [i] would yield (148, 196, 2782)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 100757 595200 826054 429219 226644 917864 496450 674683 025618 187799 > 2¹⁹⁶ [i]