MinT - Best Known (72−55, 72, s)-Nets in Base 2

Best Known (72−55, 72, s)-Nets in Base 2

(72−55, 72, 17)-Net over F₂ — Constructive and digital

Digital (17, 72, 17)-net over F₂, using

t-expansion [i] based on digital (15, 72, 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]

(72−55, 72, 29)-Net in Base 2 — Upper bound on s

There is no (17, 72, 30)-net in base 2, because

17 times m-reduction [i] would yield (17, 55, 30)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁵⁵, 30, S₂, 2, 38), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 576460 752303 423488 / 13 > 2⁵⁵ [i]