MinT - Best Known (66−54, 66, s)-Nets in Base 2

Best Known (66−54, 66, s)-Nets in Base 2

(66−54, 66, 14)-Net over F₂ — Constructive and digital

Digital (12, 66, 14)-net over F₂, using

t-expansion [i] based on digital (11, 66, 14)-net over F₂, using
- net from sequence [i] based on digital (11, 13)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]

(66−54, 66, 19)-Net in Base 2 — Upper bound on s

There is no (12, 66, 20)-net in base 2, because

11 times m-reduction [i] would yield (12, 55, 20)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁵⁵, 20, S₂, 3, 43), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 432345 564227 567616 / 11 > 2⁵⁵ [i]