MinT - Best Known (195−41, 195, s)-Nets in Base 2

Best Known (195−41, 195, s)-Nets in Base 2

(195−41, 195, 260)-Net over F₂ — Constructive and digital

Digital (154, 195, 260)-net over F₂, using

t-expansion [i] based on digital (153, 195, 260)-net over F₂, using
- 1 times m-reduction [i] based on digital (153, 196, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 49, 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]

(195−41, 195, 438)-Net over F₂ — Digital

Digital (154, 195, 438)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−41, 195, 6877)-Net in Base 2 — Upper bound on s

There is no (154, 195, 6878)-net in base 2, because

1 times m-reduction [i] would yield (154, 194, 6878)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25131 663202 086365 691655 815672 271574 635803 791099 888742 482081 > 2¹⁹⁴ [i]