MinT - Best Known (242−98, 242, s)-Nets in Base 2

Best Known (242−98, 242, s)-Nets in Base 2

(242−98, 242, 75)-Net over F₂ — Constructive and digital

Digital (144, 242, 75)-net over F₂, using

4 times m-reduction [i] based on digital (144, 246, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 90, 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, 156, 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]

(242−98, 242, 106)-Net over F₂ — Digital

Digital (144, 242, 106)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−98, 242, 517)-Net in Base 2 — Upper bound on s

There is no (144, 242, 518)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 640040 515325 154396 459971 910600 666898 290349 115115 355404 758598 123635 696096 > 2²⁴² [i]