MinT - Best Known (252−104, 252, s)-Nets in Base 2

Best Known (252−104, 252, s)-Nets in Base 2

(252−104, 252, 75)-Net over F₂ — Constructive and digital

Digital (148, 252, 75)-net over F₂, using

6 times m-reduction [i] based on digital (148, 258, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 94, 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, 164, 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]

(252−104, 252, 105)-Net over F₂ — Digital

Digital (148, 252, 105)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−104, 252, 508)-Net in Base 2 — Upper bound on s

There is no (148, 252, 509)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7465 378113 836617 664178 091920 531810 731224 867022 334350 386431 187469 617700 342571 > 2²⁵² [i]