Best Known (9, 9+96, s)-Nets in Base 16
(9, 9+96, 65)-Net over F16 — Constructive and digital
Digital (9, 105, 65)-net over F16, using
- t-expansion [i] based on digital (6, 105, 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
(9, 9+96, 72)-Net over F16 — Digital
Digital (9, 105, 72)-net over F16, using
- net from sequence [i] based on digital (9, 71)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 9 and N(F) ≥ 72, using
(9, 9+96, 296)-Net in Base 16 — Upper bound on s
There is no (9, 105, 297)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16105, 297, S16, 96), but
- the linear programming bound shows that M ≥ 223 734205 687221 125675 813844 411092 434063 735319 768062 112771 018290 879871 650503 927451 596075 794800 973128 650948 220440 870513 142810 762999 500738 123601 721699 242906 330382 698439 793041 445111 162043 784300 366473 255989 093744 242874 908672 / 78 348464 757096 948253 933367 934053 987415 457616 019696 367524 108639 221869 581848 673393 053956 992305 > 16105 [i]