MinT - Best Known (170−66, 170, s)-Nets in Base 2

Best Known (170−66, 170, s)-Nets in Base 2

(170−66, 170, 66)-Net over F₂ — Constructive and digital

Digital (104, 170, 66)-net over F₂, using

8 times m-reduction [i] based on digital (104, 178, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 89, 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]

(170−66, 170, 86)-Net over F₂ — Digital

Digital (104, 170, 86)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−66, 170, 421)-Net in Base 2 — Upper bound on s

There is no (104, 170, 422)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1597 589666 736308 084924 092772 114766 527727 025871 793515 > 2¹⁷⁰ [i]