MinT - Best Known (123−95, 123, s)-Nets in Base 2

Best Known (123−95, 123, s)-Nets in Base 2

(123−95, 123, 21)-Net over F₂ — Constructive and digital

Digital (28, 123, 21)-net over F₂, using

t-expansion [i] based on digital (21, 123, 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]

(123−95, 123, 25)-Net over F₂ — Digital

Digital (28, 123, 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]

(123−95, 123, 39)-Net in Base 2 — Upper bound on s

There is no (28, 123, 40)-net in base 2, because

11 times m-reduction [i] would yield (28, 112, 40)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹¹², 40, S₂, 3, 84), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 1 474612 307823 891046 502660 957498 507264 / 255 > 2¹¹² [i]