MinT - Best Known (182, 182+61, s)-Nets in Base 2

Best Known (182, 182+61, s)-Nets in Base 2

(182, 182+61, 195)-Net over F₂ — Constructive and digital

Digital (182, 243, 195)-net over F₂, using

9 times m-reduction [i] based on digital (182, 252, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 84, 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]

(182, 182+61, 326)-Net over F₂ — Digital

Digital (182, 243, 326)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(182, 182+61, 3184)-Net in Base 2 — Upper bound on s

There is no (182, 243, 3185)-net in base 2, because

1 times m-reduction [i] would yield (182, 242, 3185)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 067635 371445 850378 838254 566013 268314 450205 138216 253016 236215 546763 570832 > 2²⁴² [i]