MinT - Best Known (157−62, 157, s)-Nets in Base 2

Best Known (157−62, 157, s)-Nets in Base 2

(157−62, 157, 66)-Net over F₂ — Constructive and digital

Digital (95, 157, 66)-net over F₂, using

3 times m-reduction [i] based on digital (95, 160, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 80, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(157−62, 157, 78)-Net over F₂ — Digital

Digital (95, 157, 78)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−62, 157, 371)-Net in Base 2 — Upper bound on s

There is no (95, 157, 372)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 186487 532803 240555 036297 321117 974496 334823 760728 > 2¹⁵⁷ [i]