MinT - Best Known (237−106, 237, s)-Nets in Base 2

Best Known (237−106, 237, s)-Nets in Base 2

(237−106, 237, 66)-Net over F₂ — Constructive and digital

Digital (131, 237, 66)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 92, 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, 145, 33)-net over F₂, using
  - net from sequence [i] based on digital (39, 32)-sequence over F₂ (see above)

(237−106, 237, 83)-Net over F₂ — Digital

Digital (131, 237, 83)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−106, 237, 298)-Net in Base 2 — Upper bound on s

There is no (131, 237, 299)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2²³⁷, 299, S₂, 106), but
- the linear programming bound shows that MÂ â‰¥ 2 372623 864838 720824 144751 616230 912568 605364 469958 081012 522169 374458 839809 772727 298051 538944 / 10 001354 293176 388857 > 2²³⁷ [i]