MinT - Best Known (27, 27+21, s)-Nets in Base 2

Best Known (27, 27+21, s)-Nets in Base 2

(27, 27+21, 28)-Net over F₂ — Constructive and digital

Digital (27, 48, 28)-net over F₂, using

trace code for nets [i] based on digital (3, 24, 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]

(27, 27+21, 103)-Net in Base 2 — Upper bound on s

There is no (27, 48, 104)-net in base 2, because

1 times m-reduction [i] would yield (27, 47, 104)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 141 176001 752124 > 2⁴⁷ [i]