MinT - Best Known (41, 41+212, s)-Nets in Base 2

Best Known (41, 41+212, s)-Nets in Base 2

(41, 41+212, 33)-Net over F₂ — Constructive and digital

Digital (41, 253, 33)-net over F₂, using

t-expansion [i] based on digital (39, 253, 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]

(41, 41+212, 50)-Net in Base 2 — Upper bound on s

There is no (41, 253, 51)-net in base 2, because

8 times m-reduction [i] would yield (41, 245, 51)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²⁴⁵, 51, S₂, 5, 204), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 62532 251316 636578 192612 065146 293372 112166 310078 221906 165839 886676 148399 112192 / 1025 > 2²⁴⁵ [i]