MinT - Best Known (188−36, 188, s)-Nets in Base 2

Best Known (188−36, 188, s)-Nets in Base 2

(188−36, 188, 266)-Net over F₂ — Constructive and digital

Digital (152, 188, 266)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (2, 20, 6)-net over F₂, using
  - net from sequence [i] based on digital (2, 5)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (132, 168, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 42, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(188−36, 188, 570)-Net over F₂ — Digital

Digital (152, 188, 570)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−36, 188, 10498)-Net in Base 2 — Upper bound on s

There is no (152, 188, 10499)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 392 650098 977351 345313 966521 003401 655598 114952 445352 501808 > 2¹⁸⁸ [i]