MinT - Best Known (215−53, 215, s)-Nets in Base 2

Best Known (215−53, 215, s)-Nets in Base 2

(215−53, 215, 195)-Net over F₂ — Constructive and digital

Digital (162, 215, 195)-net over F₂, using

7 times m-reduction [i] based on digital (162, 222, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 74, 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]

(215−53, 215, 309)-Net over F₂ — Digital

Digital (162, 215, 309)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−53, 215, 3131)-Net in Base 2 — Upper bound on s

There is no (162, 215, 3132)-net in base 2, because

1 times m-reduction [i] would yield (162, 214, 3132)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26481 727066 153499 005902 787890 295690 502576 768532 889137 130818 141721 > 2²¹⁴ [i]