MinT - Best Known (163, 163+67, s)-Nets in Base 2

Best Known (163, 163+67, s)-Nets in Base 2

(163, 163+67, 135)-Net over F₂ — Constructive and digital

Digital (163, 230, 135)-net over F₂, using

1 times m-reduction [i] based on digital (163, 231, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 77, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(163, 163+67, 216)-Net over F₂ — Digital

Digital (163, 230, 216)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+67, 1567)-Net in Base 2 — Upper bound on s

There is no (163, 230, 1568)-net in base 2, because

1 times m-reduction [i] would yield (163, 229, 1568)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 876 621943 712172 896314 665866 941540 021623 147897 392779 117223 787978 441840 > 2²²⁹ [i]