Best Known (7, 7+72, s)-Nets in Base 16
(7, 7+72, 65)-Net over F16 — Constructive and digital
Digital (7, 79, 65)-net over F16, using
- t-expansion [i] based on digital (6, 79, 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
(7, 7+72, 279)-Net in Base 16 — Upper bound on s
There is no (7, 79, 280)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1679, 280, S16, 72), but
- the linear programming bound shows that M ≥ 188 343775 767451 348342 236670 498440 076703 510774 936977 194527 755786 566654 323144 360409 376535 740663 015424 862640 214402 597161 360534 880941 597045 234130 465245 477235 326976 / 1406 803574 783897 311796 156455 194829 117401 103093 191133 624304 542401 > 1679 [i]