MinT - Best Known (131, 131+76, s)-Nets in Base 2

Best Known (131, 131+76, s)-Nets in Base 2

(131, 131+76, 75)-Net over F₂ — Constructive and digital

Digital (131, 207, 75)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 77, 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, 130, 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]

(131, 131+76, 84)-Net in Base 2 — Constructive

(131, 207, 84)-net in base 2, using

1 times m-reduction [i] based on (131, 208, 84)-net in base 2, using
- trace code for nets [i] based on (27, 104, 42)-net in base 4, using
  - net from sequence [i] based on (27, 41)-sequence in base 4, using
    - base expansion [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]

(131, 131+76, 115)-Net over F₂ — Digital

Digital (131, 207, 115)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+76, 601)-Net in Base 2 — Upper bound on s

There is no (131, 207, 602)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 215 398599 883170 621410 311580 579712 263608 789512 621559 759754 138040 > 2²⁰⁷ [i]