MinT - Best Known (195, 195+57, s)-Nets in Base 2

Best Known (195, 195+57, s)-Nets in Base 2

(195, 195+57, 260)-Net over F₂ — Constructive and digital

Digital (195, 252, 260)-net over F₂, using

trace code for nets [i] based on digital (6, 63, 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, 195+57, 444)-Net over F₂ — Digital

Digital (195, 252, 444)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(195, 195+57, 5601)-Net in Base 2 — Upper bound on s

There is no (195, 252, 5602)-net in base 2, because

1 times m-reduction [i] would yield (195, 251, 5602)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3621 747807 292838 272755 883365 398999 170809 419516 214250 814145 040495 036685 558920 > 2²⁵¹ [i]