MinT - Best Known (227−200, 227, s)-Nets in Base 2

Best Known (227−200, 227, s)-Nets in Base 2

(227−200, 227, 21)-Net over F₂ — Constructive and digital

Digital (27, 227, 21)-net over F₂, using

t-expansion [i] based on digital (21, 227, 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]

(227−200, 227, 24)-Net over F₂ — Digital

Digital (27, 227, 24)-net over F₂, using

t-expansion [i] based on digital (25, 227, 24)-net over F₂, using
- net from sequence [i] based on digital (25, 23)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 25 and N(F) ≥ 24, using
    - Drinfeld modules of rank 1 [i]

(227−200, 227, 34)-Net in Base 2 — Upper bound on s

There is no (27, 227, 35)-net in base 2, because

24 times m-reduction [i] would yield (27, 203, 35)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²⁰³, 35, S₂, 6, 176), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 797 041269 952459 176668 813197 801216 650851 012684 916265 246309 482496 / 59 > 2²⁰³ [i]