Best Known (7, 7+91, s)-Nets in Base 16
(7, 7+91, 65)-Net over F16 — Constructive and digital
Digital (7, 98, 65)-net over F16, using
- t-expansion [i] based on digital (6, 98, 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+91, 196)-Net in Base 16 — Upper bound on s
There is no (7, 98, 197)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1698, 197, S16, 91), but
- the linear programming bound shows that M ≥ 29037 547997 045708 632720 478676 332246 072211 963433 053868 293809 437597 782753 125452 104611 712621 112663 656191 041197 667218 716415 037309 684889 686957 774521 205559 491687 570885 128357 047827 855417 802752 / 2 770390 633880 893781 269685 436230 737819 543155 013599 073907 235967 182247 > 1698 [i]