MinT - Best Known (199−43, 199, s)-Nets in Base 2

Best Known (199−43, 199, s)-Nets in Base 2

(199−43, 199, 260)-Net over F₂ — Constructive and digital

Digital (156, 199, 260)-net over F₂, using

1 times m-reduction [i] based on digital (156, 200, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 50, 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]

(199−43, 199, 411)-Net over F₂ — Digital

Digital (156, 199, 411)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−43, 199, 5950)-Net in Base 2 — Upper bound on s

There is no (156, 199, 5951)-net in base 2, because

1 times m-reduction [i] would yield (156, 198, 5951)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 403013 218852 903577 563351 089817 638462 590581 696113 819925 632412 > 2¹⁹⁸ [i]