MinT - Best Known (55, 55+155, s)-Nets in Base 2

Best Known (55, 55+155, s)-Nets in Base 2

(55, 55+155, 42)-Net over F₂ — Constructive and digital

Digital (55, 210, 42)-net over F₂, using

t-expansion [i] based on digital (54, 210, 42)-net over F₂, using
- net from sequence [i] based on digital (54, 41)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(55, 55+155, 71)-Net in Base 2 — Upper bound on s

There is no (55, 210, 72)-net in base 2, because

3 times m-reduction [i] would yield (55, 207, 72)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²⁰⁷, 72, S₂, 3, 152), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 116830 823569 805628 993002 811961 571885 853774 246459 984170 297751 240704 / 459 > 2²⁰⁷ [i]