MinT - Best Known (56, 56+39, s)-Nets in Base 2

Best Known (56, 56+39, s)-Nets in Base 2

(56, 56+39, 42)-Net over F₂ — Constructive and digital

Digital (56, 95, 42)-net over F₂, using

t-expansion [i] based on digital (54, 95, 42)-net over F₂, using
- net from sequence [i] based on digital (54, 41)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(56, 56+39, 48)-Net over F₂ — Digital

Digital (56, 95, 48)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+39, 218)-Net in Base 2 — Upper bound on s

There is no (56, 95, 219)-net in base 2, because

1 times m-reduction [i] would yield (56, 94, 219)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 21397 996343 499114 180889 986946 > 2⁹⁴ [i]