MinT - Best Known (213−193, 213, s)-Nets in Base 2

Best Known (213−193, 213, s)-Nets in Base 2

(213−193, 213, 20)-Net over F₂ — Constructive and digital

Digital (20, 213, 20)-net over F₂, using

t-expansion [i] based on digital (19, 213, 20)-net over F₂, using
- net from sequence [i] based on digital (19, 19)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
    - an explicitly constructive algebraic function field [i]

(213−193, 213, 27)-Net in Base 2 — Upper bound on s

There is no (20, 213, 28)-net in base 2, because

80 times m-reduction [i] would yield (20, 133, 28)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹³³, 28, S₂, 5, 113), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 261336 857795 280739 939871 698507 597986 398208 / 19 > 2¹³³ [i]