MinT - Best Known (85−65, 85, s)-Nets in Base 2

Best Known (85−65, 85, s)-Nets in Base 2

(85−65, 85, 20)-Net over F₂ — Constructive and digital

Digital (20, 85, 20)-net over F₂, using

t-expansion [i] based on digital (19, 85, 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]

(85−65, 85, 29)-Net in Base 2 — Upper bound on s

There is no (20, 85, 30)-net in base 2, because

1 times m-reduction [i] would yield (20, 84, 30)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁸⁴, 30, S₂, 3, 64), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 309 485009 821345 068724 781056 / 13 > 2⁸⁴ [i]