MinT - Best Known (212−184, 212, s)-Nets in Base 2

Best Known (212−184, 212, s)-Nets in Base 2

(212−184, 212, 21)-Net over F₂ — Constructive and digital

Digital (28, 212, 21)-net over F₂, using

t-expansion [i] based on digital (21, 212, 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]

(212−184, 212, 25)-Net over F₂ — Digital

Digital (28, 212, 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]

(212−184, 212, 35)-Net in Base 2 — Upper bound on s

There is no (28, 212, 36)-net in base 2, because

3 times m-reduction [i] would yield (28, 209, 36)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²⁰⁹, 36, S₂, 6, 181), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 75693 209636 775477 939128 582397 638123 229205 849819 144673 714036 015104 / 91 > 2²⁰⁹ [i]