MinT - Best Known (159, 159+43, s)-Nets in Base 2

Best Known (159, 159+43, s)-Nets in Base 2

(159, 159+43, 260)-Net over F₂ — Constructive and digital

Digital (159, 202, 260)-net over F₂, using

2 times m-reduction [i] based on digital (159, 204, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 51, 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]

(159, 159+43, 435)-Net over F₂ — Digital

Digital (159, 202, 435)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 159+43, 6572)-Net in Base 2 — Upper bound on s

There is no (159, 202, 6573)-net in base 2, because

1 times m-reduction [i] would yield (159, 201, 6573)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 217459 078295 426908 753666 632599 473281 632324 637310 848016 954684 > 2²⁰¹ [i]