MinT - Best Known (180, 180+65, s)-Nets in Base 2

Best Known (180, 180+65, s)-Nets in Base 2

(180, 180+65, 195)-Net over F₂ — Constructive and digital

Digital (180, 245, 195)-net over F₂, using

4 times m-reduction [i] based on digital (180, 249, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 83, 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]

(180, 180+65, 285)-Net over F₂ — Digital

Digital (180, 245, 285)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+65, 2477)-Net in Base 2 — Upper bound on s

There is no (180, 245, 2478)-net in base 2, because

1 times m-reduction [i] would yield (180, 244, 2478)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28 360539 770125 263305 427415 296663 211509 064689 810094 618252 414800 851190 182121 > 2²⁴⁴ [i]