MinT - Best Known (147, 147+54, s)-Nets in Base 2

Best Known (147, 147+54, s)-Nets in Base 2

(147, 147+54, 144)-Net over F₂ — Constructive and digital

Digital (147, 201, 144)-net over F₂, using

3 times m-reduction [i] based on digital (147, 204, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 68, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(147, 147+54, 234)-Net over F₂ — Digital

Digital (147, 201, 234)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+54, 1863)-Net in Base 2 — Upper bound on s

There is no (147, 201, 1864)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 248511 700445 580090 956847 172369 776956 989780 857250 966328 255384 > 2²⁰¹ [i]