MinT - Best Known (150, 150+107, s)-Nets in Base 2

Best Known (150, 150+107, s)-Nets in Base 2

(150, 150+107, 75)-Net over F₂ — Constructive and digital

Digital (150, 257, 75)-net over F₂, using

t-expansion [i] based on digital (148, 257, 75)-net over F₂, using
- 1 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]

(150, 150+107, 104)-Net over F₂ — Digital

Digital (150, 257, 104)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+107, 511)-Net in Base 2 — Upper bound on s

There is no (150, 257, 512)-net in base 2, because

1 times m-reduction [i] would yield (150, 256, 512)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 121826 616136 858940 201882 759917 628490 576580 406669 244441 745528 972923 136524 863665 > 2²⁵⁶ [i]