MinT - Best Known (163, 163+65, s)-Nets in Base 2

Best Known (163, 163+65, s)-Nets in Base 2

(163, 163+65, 144)-Net over F₂ — Constructive and digital

Digital (163, 228, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 76, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(163, 163+65, 226)-Net over F₂ — Digital

Digital (163, 228, 226)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+65, 1700)-Net in Base 2 — Upper bound on s

There is no (163, 228, 1701)-net in base 2, because

1 times m-reduction [i] would yield (163, 227, 1701)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 219 027438 038030 287324 367472 869897 691834 237101 000060 159350 358961 208885 > 2²²⁷ [i]