MinT - Best Known (90−73, 90, s)-Nets in Base 2

Best Known (90−73, 90, s)-Nets in Base 2

(90−73, 90, 17)-Net over F₂ — Constructive and digital

Digital (17, 90, 17)-net over F₂, using

t-expansion [i] based on digital (15, 90, 17)-net over F₂, using
- net from sequence [i] based on digital (15, 16)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]

(90−73, 90, 26)-Net in Base 2 — Upper bound on s

There is no (17, 90, 27)-net in base 2, because

17 times m-reduction [i] would yield (17, 73, 27)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁷³, 27, S₂, 3, 56), but
  - the LP bound with quadratic polynomials shows that MÂ â‰¥ 1 888946 593147 858085 478400 / 171 > 2⁷³ [i]