MinT - Best Known (163−120, 163, s)-Nets in Base 2

Best Known (163−120, 163, s)-Nets in Base 2

(163−120, 163, 33)-Net over F₂ — Constructive and digital

Digital (43, 163, 33)-net over F₂, using

t-expansion [i] based on digital (39, 163, 33)-net over F₂, using
- net from sequence [i] based on digital (39, 32)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(163−120, 163, 34)-Net over F₂ — Digital

Digital (43, 163, 34)-net over F₂, using

net from sequence [i] based on digital (43, 33)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 43 and N(F) ≥ 34, using
  - a curve from the manYPoints database [i]

(163−120, 163, 65)-Net in Base 2 — Upper bound on s

There is no (43, 163, 66)-net in base 2, because

37 times m-reduction [i] would yield (43, 126, 66)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹²⁶, 66, S₂, 2, 83), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 680 564733 841876 926926 749214 863536 422912 / 7 > 2¹²⁶ [i]