MinT - Best Known (165, 165+61, s)-Nets in Base 2

Best Known (165, 165+61, s)-Nets in Base 2

(165, 165+61, 195)-Net over F₂ — Constructive and digital

Digital (165, 226, 195)-net over F₂, using

2¹ times duplication [i] based on digital (164, 225, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 75, 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]

(165, 165+61, 255)-Net over F₂ — Digital

Digital (165, 226, 255)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+61, 2136)-Net in Base 2 — Upper bound on s

There is no (165, 226, 2137)-net in base 2, because

1 times m-reduction [i] would yield (165, 225, 2137)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 54 518175 275212 676765 056944 197101 277448 061641 082269 113746 267282 812768 > 2²²⁵ [i]