MinT - Best Known (213−80, 213, s)-Nets in Base 2

Best Known (213−80, 213, s)-Nets in Base 2

(213−80, 213, 75)-Net over F₂ — Constructive and digital

Digital (133, 213, 75)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 79, 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, 134, 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]

(213−80, 213, 112)-Net over F₂ — Digital

Digital (133, 213, 112)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−80, 213, 575)-Net in Base 2 — Upper bound on s

There is no (133, 213, 576)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14005 731124 852868 957174 782969 921124 167076 735122 766533 218774 901195 > 2²¹³ [i]