MinT - Best Known (125−50, 125, s)-Nets in Base 2

Best Known (125−50, 125, s)-Nets in Base 2

(125−50, 125, 56)-Net over F₂ — Constructive and digital

Digital (75, 125, 56)-net over F₂, using

1 times m-reduction [i] based on digital (75, 126, 56)-net over F₂, using
- trace code for nets [i] based on digital (12, 63, 28)-net over F₄, using
  - net from sequence [i] based on digital (12, 27)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]

(125−50, 125, 63)-Net over F₂ — Digital

Digital (75, 125, 63)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−50, 125, 290)-Net in Base 2 — Upper bound on s

There is no (75, 125, 291)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 44 297343 303118 549012 912701 007864 618768 > 2¹²⁵ [i]