MinT - Best Known (127−107, 127, s)-Nets in Base 2

Best Known (127−107, 127, s)-Nets in Base 2

(127−107, 127, 20)-Net over F₂ — Constructive and digital

Digital (20, 127, 20)-net over F₂, using

t-expansion [i] based on digital (19, 127, 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]

(127−107, 127, 28)-Net in Base 2 — Upper bound on s

There is no (20, 127, 29)-net in base 2, because

18 times m-reduction [i] would yield (20, 109, 29)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁰⁹, 29, S₂, 4, 89), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 49326 820156 080862 471039 715127 590912 / 45 > 2¹⁰⁹ [i]