MinT - Best Known (142−36, 142, s)-Nets in Base 2

Best Known (142−36, 142, s)-Nets in Base 2

(142−36, 142, 144)-Net over F₂ — Constructive and digital

Digital (106, 142, 144)-net over F₂, using

2¹ times duplication [i] based on digital (105, 141, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 47, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(142−36, 142, 205)-Net over F₂ — Digital

Digital (106, 142, 205)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−36, 142, 1763)-Net in Base 2 — Upper bound on s

There is no (106, 142, 1764)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 577304 085643 322424 523021 641640 786203 037214 > 2¹⁴² [i]