MinT - Best Known (181−46, 181, s)-Nets in Base 2

Best Known (181−46, 181, s)-Nets in Base 2

(181−46, 181, 195)-Net over F₂ — Constructive and digital

Digital (135, 181, 195)-net over F₂, using

2¹ times duplication [i] based on digital (134, 180, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 60, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(181−46, 181, 247)-Net over F₂ — Digital

Digital (135, 181, 247)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−46, 181, 2171)-Net in Base 2 — Upper bound on s

There is no (135, 181, 2172)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 085730 975691 934228 952065 770070 786634 689189 906104 966670 > 2¹⁸¹ [i]