MinT - Best Known (53−23, 53, s)-Nets in Base 2

Best Known (53−23, 53, s)-Nets in Base 2

(53−23, 53, 28)-Net over F₂ — Constructive and digital

Digital (30, 53, 28)-net over F₂, using

1 times m-reduction [i] based on digital (30, 54, 28)-net over F₂, using
- trace code for nets [i] based on digital (3, 27, 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]

(53−23, 53, 29)-Net over F₂ — Digital

Digital (30, 53, 29)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(53−23, 53, 114)-Net in Base 2 — Upper bound on s

There is no (30, 53, 115)-net in base 2, because

1 times m-reduction [i] would yield (30, 52, 115)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4554 507082 181948 > 2⁵² [i]