MinT - Best Known (105−49, 105, s)-Nets in Base 2

Best Known (105−49, 105, s)-Nets in Base 2

(105−49, 105, 42)-Net over F₂ — Constructive and digital

Digital (56, 105, 42)-net over F₂, using

t-expansion [i] based on digital (54, 105, 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]

(105−49, 105, 139)-Net in Base 2 — Upper bound on s

There is no (56, 105, 140)-net in base 2, because

1 times m-reduction [i] would yield (56, 104, 140)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2¹⁰⁴, 140, S₂, 48), but
  - the linear programming bound shows that MÂ â‰¥ 906615 640616 170781 657520 759485 197602 258944 / 38102 739675 > 2¹⁰⁴ [i]