MinT - Best Known (137, 137+122, s)-Nets in Base 2

Best Known (137, 137+122, s)-Nets in Base 2

(137, 137+122, 63)-Net over F₂ — Constructive and digital

Digital (137, 259, 63)-net over F₂, using

t-expansion [i] based on digital (136, 259, 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, 177, 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]

(137, 137+122, 81)-Net over F₂ — Digital

Digital (137, 259, 81)-net over F₂, using

t-expansion [i] based on digital (126, 259, 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]

(137, 137+122, 363)-Net in Base 2 — Upper bound on s

There is no (137, 259, 364)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 966245 715120 787331 154932 340518 389797 764310 950939 196375 107014 049761 159219 636400 > 2²⁵⁹ [i]