MinT - Best Known (47−19, 47, s)-Nets in Base 2

Best Known (47−19, 47, s)-Nets in Base 2

(47−19, 47, 30)-Net over F₂ — Constructive and digital

Digital (28, 47, 30)-net over F₂, using

1 times m-reduction [i] based on digital (28, 48, 30)-net over F₂, using
- trace code for nets [i] based on digital (4, 24, 15)-net over F₄, using
  - net from sequence [i] based on digital (4, 14)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
      - an explicitly constructive algebraic function field [i]

(47−19, 47, 31)-Net over F₂ — Digital

Digital (28, 47, 31)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(47−19, 47, 130)-Net in Base 2 — Upper bound on s

There is no (28, 47, 131)-net in base 2, because

1 times m-reduction [i] would yield (28, 46, 131)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 71 095888 176448 > 2⁴⁶ [i]