MinT - Best Known (106, 106+46, s)-Nets in Base 2

Best Known (106, 106+46, s)-Nets in Base 2

(106, 106+46, 76)-Net over F₂ — Constructive and digital

Digital (106, 152, 76)-net over F₂, using

1 times m-reduction [i] based on digital (106, 153, 76)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (6, 29, 10)-net over F₂, using
    - net from sequence [i] based on digital (6, 9)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]
    - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
  2. digital (77, 124, 66)-net over F₂, using
    - trace code for nets [i] based on digital (15, 62, 33)-net over F₄, using
      - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
        an explicitly constructive algebraic function field [i]

(106, 106+46, 86)-Net in Base 2 — Constructive

(106, 152, 86)-net in base 2, using

trace code for nets [i] based on (30, 76, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
  - base expansion [i] based on digital (60, 42)-sequence over F₂, using
    - t-expansion [i] based on digital (59, 42)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 54, N(F)Â =Â 42, and 1 place with degree 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]

(106, 106+46, 140)-Net over F₂ — Digital

Digital (106, 152, 140)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+46, 886)-Net in Base 2 — Upper bound on s

There is no (106, 152, 887)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5746 256868 009142 816301 956323 512011 335451 676490 > 2¹⁵² [i]