MinT - Best Known (193−181, 193, s)-Nets in Base 2

Best Known (193−181, 193, s)-Nets in Base 2

(193−181, 193, 14)-Net over F₂ — Constructive and digital

Digital (12, 193, 14)-net over F₂, using

t-expansion [i] based on digital (11, 193, 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]

(193−181, 193, 18)-Net in Base 2 — Upper bound on s

There is no (12, 193, 19)-net in base 2, because

104 times m-reduction [i] would yield (12, 89, 19)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁸⁹, 19, S₂, 5, 77), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 9284 550294 640352 061743 431680 / 13 > 2⁸⁹ [i]