MinT - Best Known (172−46, 172, s)-Nets in Base 2

Best Known (172−46, 172, s)-Nets in Base 2

(172−46, 172, 144)-Net over F₂ — Constructive and digital

Digital (126, 172, 144)-net over F₂, using

2¹ times duplication [i] based on digital (125, 171, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 57, 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]

(172−46, 172, 208)-Net over F₂ — Digital

Digital (126, 172, 208)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−46, 172, 1647)-Net in Base 2 — Upper bound on s

There is no (126, 172, 1648)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6020 887781 073811 759675 758204 428450 250378 000292 930118 > 2¹⁷² [i]