MinT - Best Known (254−118, 254, s)-Nets in Base 2

Best Known (254−118, 254, s)-Nets in Base 2

(254−118, 254, 63)-Net over F₂ — Constructive and digital

Digital (136, 254, 63)-net over F₂, using

4 times m-reduction [i] based on digital (136, 258, 63)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (21, 82, 21)-net over F₂, using
    - net from sequence [i] based on digital (21, 20)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
        an explicitly constructive algebraic function field [i]
  2. digital (54, 176, 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]

(254−118, 254, 81)-Net over F₂ — Digital

Digital (136, 254, 81)-net over F₂, using

t-expansion [i] based on digital (126, 254, 81)-net over F₂, using
- net from sequence [i] based on digital (126, 80)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 126 and N(F) ≥ 81, using
    - Drinfeld modules of rank 1 [i]

(254−118, 254, 370)-Net in Base 2 — Upper bound on s

There is no (136, 254, 371)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 32048 199726 747781 228938 147459 413795 076825 602872 733920 748961 069323 280907 521296 > 2²⁵⁴ [i]