MinT - Best Known (260−101, 260, s)-Nets in Base 2

Best Known (260−101, 260, s)-Nets in Base 2

(260−101, 260, 84)-Net over F₂ — Constructive and digital

Digital (159, 260, 84)-net over F₂, using

2¹ times duplication [i] based on digital (158, 259, 84)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (54, 104, 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]
  2. digital (54, 155, 42)-net over F₂, using
    - net from sequence [i] based on digital (54, 41)-sequence over F₂ (see above)

(260−101, 260, 123)-Net over F₂ — Digital

Digital (159, 260, 123)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−101, 260, 635)-Net in Base 2 — Upper bound on s

There is no (159, 260, 636)-net in base 2, because

1 times m-reduction [i] would yield (159, 259, 636)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 979441 190544 353076 530705 057866 642932 587346 893773 148684 238494 046824 322332 716959 > 2²⁵⁹ [i]