MinT - Best Known (190−80, 190, s)-Nets in Base 2

Best Known (190−80, 190, s)-Nets in Base 2

(190−80, 190, 66)-Net over F₂ — Constructive and digital

Digital (110, 190, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 95, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(190−80, 190, 79)-Net over F₂ — Digital

Digital (110, 190, 79)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−80, 190, 368)-Net in Base 2 — Upper bound on s

There is no (110, 190, 369)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1668 359382 846885 847229 606057 619311 890186 314612 299550 773238 > 2¹⁹⁰ [i]