MinT - Best Known (68, 68+32, s)-Nets in Base 2

Best Known (68, 68+32, s)-Nets in Base 2

(68, 68+32, 66)-Net over F₂ — Constructive and digital

Digital (68, 100, 66)-net over F₂, using

6 times m-reduction [i] based on digital (68, 106, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 53, 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]

(68, 68+32, 88)-Net over F₂ — Digital

Digital (68, 100, 88)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+32, 494)-Net in Base 2 — Upper bound on s

There is no (68, 100, 495)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 285389 986419 288493 745505 784678 > 2¹⁰⁰ [i]