MinT - Best Known (157−43, 157, s)-Nets in Base 2

Best Known (157−43, 157, s)-Nets in Base 2

(157−43, 157, 135)-Net over F₂ — Constructive and digital

Digital (114, 157, 135)-net over F₂, using

2¹ times duplication [i] based on digital (113, 156, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 52, 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]

(157−43, 157, 182)-Net over F₂ — Digital

Digital (114, 157, 182)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−43, 157, 1464)-Net in Base 2 — Upper bound on s

There is no (114, 157, 1465)-net in base 2, because

1 times m-reduction [i] would yield (114, 156, 1465)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 91929 329079 756305 966981 734614 985941 997701 600244 > 2¹⁵⁶ [i]