MinT - Best Known (163, 163+49, s)-Nets in Base 2

Best Known (163, 163+49, s)-Nets in Base 2

(163, 163+49, 195)-Net over F₂ — Constructive and digital

Digital (163, 212, 195)-net over F₂, using

t-expansion [i] based on digital (162, 212, 195)-net over F₂, using
- 10 times m-reduction [i] based on digital (162, 222, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 74, 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]

(163, 163+49, 361)-Net over F₂ — Digital

Digital (163, 212, 361)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+49, 4308)-Net in Base 2 — Upper bound on s

There is no (163, 212, 4309)-net in base 2, because

1 times m-reduction [i] would yield (163, 211, 4309)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3292 554903 649291 767034 506346 293254 505651 811513 845689 845799 625896 > 2²¹¹ [i]