MinT - Best Known (202−84, 202, s)-Nets in Base 2

Best Known (202−84, 202, s)-Nets in Base 2

(202−84, 202, 66)-Net over F₂ — Constructive and digital

Digital (118, 202, 66)-net over F₂, using

4 times m-reduction [i] based on digital (118, 206, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 103, 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]

(202−84, 202, 85)-Net over F₂ — Digital

Digital (118, 202, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−84, 202, 404)-Net in Base 2 — Upper bound on s

There is no (118, 202, 405)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 959973 622866 233028 906531 194548 215880 281119 884793 062472 141104 > 2²⁰² [i]