MinT - Best Known (68−24, 68, s)-Nets in Base 2

Best Known (68−24, 68, s)-Nets in Base 2

(68−24, 68, 54)-Net over F₂ — Constructive and digital

Digital (44, 68, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 34, 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]

(68−24, 68, 251)-Net in Base 2 — Upper bound on s

There is no (44, 68, 252)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 299 761361 620065 180572 > 2⁶⁸ [i]