MinT - Best Known (246−100, 246, s)-Nets in Base 2

Best Known (246−100, 246, s)-Nets in Base 2

(246−100, 246, 75)-Net over F₂ — Constructive and digital

Digital (146, 246, 75)-net over F₂, using

6 times m-reduction [i] based on digital (146, 252, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 92, 33)-net over F₂, using
    - net from sequence [i] based on digital (39, 32)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
        an explicitly constructive algebraic function field [i]
  2. digital (54, 160, 42)-net over F₂, using
    - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
        an explicitly constructive algebraic function field [i]

(246−100, 246, 106)-Net over F₂ — Digital

Digital (146, 246, 106)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−100, 246, 519)-Net in Base 2 — Upper bound on s

There is no (146, 246, 520)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 119 384845 875666 188233 656246 575782 058253 531835 540848 439054 118019 522264 894624 > 2²⁴⁶ [i]