MinT - Best Known (142−56, 142, s)-Nets in Base 2

Best Known (142−56, 142, s)-Nets in Base 2

(142−56, 142, 66)-Net over F₂ — Constructive and digital

Digital (86, 142, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 71, 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]

(142−56, 142, 72)-Net over F₂ — Digital

Digital (86, 142, 72)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−56, 142, 340)-Net in Base 2 — Upper bound on s

There is no (86, 142, 341)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 853238 070789 200260 017309 015279 888616 506040 > 2¹⁴² [i]