MinT - Best Known (205−43, 205, s)-Nets in Base 2

Best Known (205−43, 205, s)-Nets in Base 2

(205−43, 205, 260)-Net over F₂ — Constructive and digital

Digital (162, 205, 260)-net over F₂, using

3 times m-reduction [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]

(205−43, 205, 459)-Net over F₂ — Digital

Digital (162, 205, 459)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−43, 205, 7260)-Net in Base 2 — Upper bound on s

There is no (162, 205, 7261)-net in base 2, because

1 times m-reduction [i] would yield (162, 204, 7261)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25 784632 852954 053065 824391 394042 888614 074536 863288 029065 633178 > 2²⁰⁴ [i]