MinT - Best Known (248−65, 248, s)-Nets in Base 2

Best Known (248−65, 248, s)-Nets in Base 2

(248−65, 248, 195)-Net over F₂ — Constructive and digital

Digital (183, 248, 195)-net over F₂, using

t-expansion [i] based on digital (182, 248, 195)-net over F₂, using
- 4 times m-reduction [i] based on digital (182, 252, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 84, 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]

(248−65, 248, 297)-Net over F₂ — Digital

Digital (183, 248, 297)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−65, 248, 2647)-Net in Base 2 — Upper bound on s

There is no (183, 248, 2648)-net in base 2, because

1 times m-reduction [i] would yield (183, 247, 2648)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 228 206694 307735 101747 373896 084894 211343 076819 089250 691028 825328 053370 362866 > 2²⁴⁷ [i]