MinT - Best Known (114−56, 114, s)-Nets in Base 2

Best Known (114−56, 114, s)-Nets in Base 2

(114−56, 114, 42)-Net over F₂ — Constructive and digital

Digital (58, 114, 42)-net over F₂, using

t-expansion [i] based on digital (54, 114, 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]

(114−56, 114, 129)-Net in Base 2 — Upper bound on s

There is no (58, 114, 130)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2¹¹⁴, 130, S₂, 56), but
- the linear programming bound shows that MÂ â‰¥ 76811 433578 425041 089555 846688 890131 841024 / 3 537275 > 2¹¹⁴ [i]