MinT - Best Known (110, 110+81, s)-Nets in Base 2

Best Known (110, 110+81, s)-Nets in Base 2

(110, 110+81, 60)-Net over F₂ — Constructive and digital

Digital (110, 191, 60)-net over F₂, using

3 times m-reduction [i] based on digital (110, 194, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 97, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(110, 110+81, 78)-Net over F₂ — Digital

Digital (110, 191, 78)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 110+81, 368)-Net in Base 2 — Upper bound on s

There is no (110, 191, 369)-net in base 2, because

1 times m-reduction [i] would yield (110, 190, 369)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1668 359382 846885 847229 606057 619311 890186 314612 299550 773238 > 2¹⁹⁰ [i]