MinT - Best Known (67−51, 67, s)-Nets in Base 2

Best Known (67−51, 67, s)-Nets in Base 2

(67−51, 67, 17)-Net over F₂ — Constructive and digital

Digital (16, 67, 17)-net over F₂, using

t-expansion [i] based on digital (15, 67, 17)-net over F₂, using
- net from sequence [i] based on digital (15, 16)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]

(67−51, 67, 28)-Net in Base 2 — Upper bound on s

There is no (16, 67, 29)-net in base 2, because

15 times m-reduction [i] would yield (16, 52, 29)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁵², 29, S₂, 2, 36), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 216172 782113 783808 / 37 > 2⁵² [i]