MinT - Best Known (95−37, 95, s)-Nets in Base 2

Best Known (95−37, 95, s)-Nets in Base 2

(95−37, 95, 54)-Net over F₂ — Constructive and digital

Digital (58, 95, 54)-net over F₂, using

1 times m-reduction [i] based on digital (58, 96, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 48, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(95−37, 95, 256)-Net in Base 2 — Upper bound on s

There is no (58, 95, 257)-net in base 2, because

1 times m-reduction [i] would yield (58, 94, 257)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 20413 753719 515103 890090 434880 > 2⁹⁴ [i]