MinT - Best Known (138, 138+88, s)-Nets in Base 2

Best Known (138, 138+88, s)-Nets in Base 2

(138, 138+88, 75)-Net over F₂ — Constructive and digital

Digital (138, 226, 75)-net over F₂, using

2 times m-reduction [i] based on digital (138, 228, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 84, 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 (54, 144, 42)-net over F₂, using
    - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
        an explicitly constructive algebraic function field [i]

(138, 138+88, 109)-Net over F₂ — Digital

Digital (138, 226, 109)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+88, 544)-Net in Base 2 — Upper bound on s

There is no (138, 226, 545)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 112 140953 598687 885521 580891 824798 352203 645516 765649 200690 285082 571904 > 2²²⁶ [i]