Best Known (109−102, 109, s)-Nets in Base 16
(109−102, 109, 65)-Net over F16 — Constructive and digital
Digital (7, 109, 65)-net over F16, using
- t-expansion [i] based on digital (6, 109, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(109−102, 109, 134)-Net in Base 16 — Upper bound on s
There is no (7, 109, 135)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16109, 135, S16, 102), but
- the linear programming bound shows that M ≥ 950991 173007 865838 708051 795440 300981 628024 499341 201352 243331 368104 595533 007945 094302 510934 869406 169459 640329 288292 033225 655866 549609 875039 920404 299776 / 5 350588 596668 443051 > 16109 [i]