MinT - Best Known (49−20, 49, s)-Nets in Base 2

Best Known (49−20, 49, s)-Nets in Base 2

(49−20, 49, 30)-Net over F₂ — Constructive and digital

Digital (29, 49, 30)-net over F₂, using

1 times m-reduction [i] based on digital (29, 50, 30)-net over F₂, using
- trace code for nets [i] based on digital (4, 25, 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]

(49−20, 49, 32)-Net over F₂ — Digital

Digital (29, 49, 32)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(49−20, 49, 121)-Net in Base 2 — Upper bound on s

There is no (29, 49, 122)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 589 666787 444736 > 2⁴⁹ [i]