MinT - Best Known (182−76, 182, s)-Nets in Base 2

Best Known (182−76, 182, s)-Nets in Base 2

(182−76, 182, 66)-Net over F₂ — Constructive and digital

Digital (106, 182, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 91, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(182−76, 182, 77)-Net over F₂ — Digital

Digital (106, 182, 77)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−76, 182, 362)-Net in Base 2 — Upper bound on s

There is no (106, 182, 363)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 551587 690573 354463 699608 631670 043061 830062 761732 456814 > 2¹⁸² [i]