MinT - Best Known (126, 223, s)-Nets in Base 2

Best Known (126, 223, s)-Nets in Base 2

(126, 223, 66)-Net over F₂ — Constructive and digital

Digital (126, 223, 66)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 87, 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 (39, 136, 33)-net over F₂, using
  - net from sequence [i] based on digital (39, 32)-sequence over F₂ (see above)

(126, 223, 84)-Net over F₂ — Digital

Digital (126, 223, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 223, 395)-Net in Base 2 — Upper bound on s

There is no (126, 223, 396)-net in base 2, because

1 times m-reduction [i] would yield (126, 222, 396)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 025479 310530 746444 787549 057427 351381 541891 266534 167595 069383 185896 > 2²²² [i]