MinT - Best Known (28, 28+59, s)-Nets in Base 2

Best Known (28, 28+59, s)-Nets in Base 2

(28, 28+59, 21)-Net over F₂ — Constructive and digital

Digital (28, 87, 21)-net over F₂, using

t-expansion [i] based on digital (21, 87, 21)-net over F₂, using
- net from sequence [i] based on digital (21, 20)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(28, 28+59, 25)-Net over F₂ — Digital

Digital (28, 87, 25)-net over F₂, using

net from sequence [i] based on digital (28, 24)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 28 and N(F) ≥ 25, using
  - a curve from the manYPoints database [i]

(28, 28+59, 45)-Net in Base 2 — Upper bound on s

There is no (28, 87, 46)-net in base 2, because

2 times m-reduction [i] would yield (28, 85, 46)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁸⁵, 46, S₂, 2, 57), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1237 940039 285380 274899 124224 / 29 > 2⁸⁵ [i]