MinT - Best Known (246−73, 246, s)-Nets in Base 2

Best Known (246−73, 246, s)-Nets in Base 2

(246−73, 246, 135)-Net over F₂ — Constructive and digital

Digital (173, 246, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 82, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(246−73, 246, 218)-Net over F₂ — Digital

Digital (173, 246, 218)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−73, 246, 1544)-Net in Base 2 — Upper bound on s

There is no (173, 246, 1545)-net in base 2, because

1 times m-reduction [i] would yield (173, 245, 1545)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 56 915801 920290 867702 183077 117285 196305 346975 269391 316346 725668 897649 810912 > 2²⁴⁵ [i]