MinT - Best Known (145, 250, s)-Nets in Base 2

Best Known (145, 250, s)-Nets in Base 2

(145, 250, 75)-Net over F₂ — Constructive and digital

Digital (145, 250, 75)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 91, 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, 159, 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]

(145, 250, 100)-Net over F₂ — Digital

Digital (145, 250, 100)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 250, 486)-Net in Base 2 — Upper bound on s

There is no (145, 250, 487)-net in base 2, because

1 times m-reduction [i] would yield (145, 249, 487)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 991 867368 077130 041346 089177 226564 313230 762528 214685 024973 934361 079572 421628 > 2²⁴⁹ [i]