Best Known (87−80, 87, s)-Nets in Base 16
(87−80, 87, 65)-Net over F16 — Constructive and digital
Digital (7, 87, 65)-net over F16, using
- t-expansion [i] based on digital (6, 87, 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
(87−80, 87, 237)-Net in Base 16 — Upper bound on s
There is no (7, 87, 238)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1687, 238, S16, 80), but
- the linear programming bound shows that M ≥ 4 424600 572317 103936 113250 842128 944848 159648 933314 468536 124285 603798 318051 113494 870287 001573 948762 286905 292159 691274 672278 203221 201998 237099 367360 559663 694846 558904 753580 414301 372416 / 7457 974225 790459 208883 326904 324727 803818 794977 755551 709413 288374 145052 307453 > 1687 [i]