MinT - Best Known (125, 216, s)-Nets in Base 2

Best Known (125, 216, s)-Nets in Base 2

(125, 216, 66)-Net over F₂ — Constructive and digital

Digital (125, 216, 66)-net over F₂, using

4 times m-reduction [i] based on digital (125, 220, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 110, 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]

(125, 216, 87)-Net over F₂ — Digital

Digital (125, 216, 87)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 216, 420)-Net in Base 2 — Upper bound on s

There is no (125, 216, 421)-net in base 2, because

1 times m-reduction [i] would yield (125, 215, 421)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 55261 765012 581299 555689 674827 958160 681359 115575 957856 299805 230688 > 2²¹⁵ [i]