MinT - Best Known (248−67, 248, s)-Nets in Base 2

Best Known (248−67, 248, s)-Nets in Base 2

(248−67, 248, 195)-Net over F₂ — Constructive and digital

Digital (181, 248, 195)-net over F₂, using

t-expansion [i] based on digital (180, 248, 195)-net over F₂, using
- 1 times m-reduction [i] based on digital (180, 249, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 83, 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]

(248−67, 248, 276)-Net over F₂ — Digital

Digital (181, 248, 276)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−67, 248, 2309)-Net in Base 2 — Upper bound on s

There is no (181, 248, 2310)-net in base 2, because

1 times m-reduction [i] would yield (181, 247, 2310)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 228 314866 601570 958482 143448 933504 582640 512992 714582 680522 247602 678081 711432 > 2²⁴⁷ [i]