MinT - Best Known (237−105, 237, s)-Nets in Base 2

Best Known (237−105, 237, s)-Nets in Base 2

(237−105, 237, 66)-Net over F₂ — Constructive and digital

Digital (132, 237, 66)-net over F₂, using

3 times m-reduction [i] based on digital (132, 240, 66)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 93, 33)-net over F₂, using
    - net from sequence [i] based on digital (39, 32)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
        an explicitly constructive algebraic function field [i]
  2. digital (39, 147, 33)-net over F₂, using
    - net from sequence [i] based on digital (39, 32)-sequence over F₂ (see above)

(237−105, 237, 84)-Net over F₂ — Digital

Digital (132, 237, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−105, 237, 397)-Net in Base 2 — Upper bound on s

There is no (132, 237, 398)-net in base 2, because

1 times m-reduction [i] would yield (132, 236, 398)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 111914 906977 984508 426171 822492 872910 813622 187017 598994 599564 588945 025112 > 2²³⁶ [i]