MinT - Best Known (163, 163+46, s)-Nets in Base 2

Best Known (163, 163+46, s)-Nets in Base 2

(163, 163+46, 260)-Net over F₂ — Constructive and digital

Digital (163, 209, 260)-net over F₂, using

2¹ times duplication [i] based on digital (162, 208, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 52, 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]

(163, 163+46, 407)-Net over F₂ — Digital

Digital (163, 209, 407)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+46, 5093)-Net in Base 2 — Upper bound on s

There is no (163, 209, 5094)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 824 347195 327337 887525 668000 068993 025998 931675 952540 728214 834856 > 2²⁰⁹ [i]