MinT - Best Known (117−60, 117, s)-Nets in Base 2

Best Known (117−60, 117, s)-Nets in Base 2

(117−60, 117, 42)-Net over F₂ — Constructive and digital

Digital (57, 117, 42)-net over F₂, using

t-expansion [i] based on digital (54, 117, 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]

(117−60, 117, 125)-Net in Base 2 — Upper bound on s

There is no (57, 117, 126)-net in base 2, because

2 times m-reduction [i] would yield (57, 115, 126)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2¹¹⁵, 126, S₂, 58), but
  - the linear programming bound shows that MÂ â‰¥ 76 098302 758686 433723 742954 201049 726976 / 1575 > 2¹¹⁵ [i]