MinT - Best Known (163, 163+57, s)-Nets in Base 2

Best Known (163, 163+57, s)-Nets in Base 2

(163, 163+57, 195)-Net over F₂ — Constructive and digital

Digital (163, 220, 195)-net over F₂, using

t-expansion [i] based on digital (162, 220, 195)-net over F₂, using
- 2 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+57, 276)-Net over F₂ — Digital

Digital (163, 220, 276)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+57, 2514)-Net in Base 2 — Upper bound on s

There is no (163, 220, 2515)-net in base 2, because

1 times m-reduction [i] would yield (163, 219, 2515)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 848179 955920 540688 603808 184292 250738 027656 511633 344691 837792 842992 > 2²¹⁹ [i]