MinT - Best Known (260−107, 260, s)-Nets in Base 2

Best Known (260−107, 260, s)-Nets in Base 2

(260−107, 260, 76)-Net over F₂ — Constructive and digital

Digital (153, 260, 76)-net over F₂, using

t-expansion [i] based on digital (152, 260, 76)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 93, 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 (59, 167, 43)-net over F₂, using
    - net from sequence [i] based on digital (59, 42)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 54, N(F)Â =Â 42, and 1 place with degree 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]

(260−107, 260, 108)-Net over F₂ — Digital

Digital (153, 260, 108)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−107, 260, 534)-Net in Base 2 — Upper bound on s

There is no (153, 260, 535)-net in base 2, because

1 times m-reduction [i] would yield (153, 259, 535)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 949016 544850 414431 050135 609494 283356 477096 261291 034174 811269 619577 961251 040448 > 2²⁵⁹ [i]