MinT - Best Known (248−73, 248, s)-Nets in Base 2

Best Known (248−73, 248, s)-Nets in Base 2

(248−73, 248, 135)-Net over F₂ — Constructive and digital

Digital (175, 248, 135)-net over F₂, using

1 times m-reduction [i] based on digital (175, 249, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 83, 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]

(248−73, 248, 224)-Net over F₂ — Digital

Digital (175, 248, 224)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−73, 248, 1607)-Net in Base 2 — Upper bound on s

There is no (175, 248, 1608)-net in base 2, because

1 times m-reduction [i] would yield (175, 247, 1608)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 229 177522 420096 968489 841654 428507 085832 920795 597819 866506 395919 340868 841682 > 2²⁴⁷ [i]