MinT - Best Known (241−71, 241, s)-Nets in Base 2

Best Known (241−71, 241, s)-Nets in Base 2

(241−71, 241, 135)-Net over F₂ — Constructive and digital

Digital (170, 241, 135)-net over F₂, using

2¹ times duplication [i] based on digital (169, 240, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 80, 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]

(241−71, 241, 218)-Net over F₂ — Digital

Digital (170, 241, 218)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−71, 241, 1561)-Net in Base 2 — Upper bound on s

There is no (170, 241, 1562)-net in base 2, because

1 times m-reduction [i] would yield (170, 240, 1562)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 800040 042436 024626 749461 274175 667087 840039 302792 213819 193937 490940 976512 > 2²⁴⁰ [i]