MinT - Best Known (57, 109, s)-Nets in Base 2

Best Known (57, 109, s)-Nets in Base 2

(57, 109, 42)-Net over F₂ — Constructive and digital

Digital (57, 109, 42)-net over F₂, using

t-expansion [i] based on digital (54, 109, 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]

(57, 109, 130)-Net in Base 2 — Upper bound on s

There is no (57, 109, 131)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2¹⁰⁹, 131, S₂, 52), but
- the linear programming bound shows that MÂ â‰¥ 1305 571891 297431 198228 222119 004417 818624 / 2 001825 > 2¹⁰⁹ [i]