Best Known (76−70, 76, s)-Nets in Base 16
(76−70, 76, 65)-Net over F16 — Constructive and digital
Digital (6, 76, 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
(76−70, 76, 224)-Net in Base 16 — Upper bound on s
There is no (6, 76, 225)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1676, 225, S16, 70), but
- the linear programming bound shows that M ≥ 39 855526 349720 323091 486860 277167 243771 023991 076211 693487 850662 045550 141843 013260 889697 866621 459002 946836 255733 132219 520669 912546 234163 164280 405174 124602 720256 / 1 215704 292369 130455 742166 059284 538512 031951 755278 298721 781379 749807 > 1676 [i]