MinT - Best Known (49−21, 49, s)-Nets in Base 2

Best Known (49−21, 49, s)-Nets in Base 2

(49−21, 49, 28)-Net over F₂ — Constructive and digital

Digital (28, 49, 28)-net over F₂, using

1 times m-reduction [i] based on digital (28, 50, 28)-net over F₂, using
- trace code for nets [i] based on digital (3, 25, 14)-net over F₄, using
  - net from sequence [i] based on digital (3, 13)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]

(49−21, 49, 112)-Net in Base 2 — Upper bound on s

There is no (28, 49, 113)-net in base 2, because

1 times m-reduction [i] would yield (28, 48, 113)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 296 059789 485408 > 2⁴⁸ [i]