MinT - Best Known (187−53, 187, s)-Nets in Base 2

Best Known (187−53, 187, s)-Nets in Base 2

(187−53, 187, 135)-Net over F₂ — Constructive and digital

Digital (134, 187, 135)-net over F₂, using

2¹ times duplication [i] based on digital (133, 186, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 62, 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]

(187−53, 187, 193)-Net over F₂ — Digital

Digital (134, 187, 193)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−53, 187, 1464)-Net in Base 2 — Upper bound on s

There is no (134, 187, 1465)-net in base 2, because

1 times m-reduction [i] would yield (134, 186, 1465)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 99 022056 279032 447521 300516 977438 500132 099740 345672 664140 > 2¹⁸⁶ [i]