Best Known (109−101, 109, s)-Nets in Base 16
(109−101, 109, 65)-Net over F16 — Constructive and digital
Digital (8, 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
(109−101, 109, 210)-Net in Base 16 — Upper bound on s
There is no (8, 109, 211)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16109, 211, S16, 101), but
- the linear programming bound shows that M ≥ 533686 144755 512872 964087 169716 792069 808827 524349 490195 770864 383488 960887 687284 039567 848257 634164 941380 817746 244302 108040 727242 060522 668935 524015 873575 880967 228862 451010 244423 416582 013374 146124 317399 140412 603048 956268 642304 / 2 999148 139903 726666 429400 005640 384112 565049 955784 371643 426252 899733 819682 913702 009483 684929 > 16109 [i]