Best Known (7, 7+87, s)-Nets in Base 16
(7, 7+87, 65)-Net over F16 — Constructive and digital
Digital (7, 94, 65)-net over F16, using
- t-expansion [i] based on digital (6, 94, 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+87, 207)-Net in Base 16 — Upper bound on s
There is no (7, 94, 208)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1694, 208, S16, 87), but
- the linear programming bound shows that M ≥ 103213 967988 925446 525528 911503 616564 414708 527971 481258 629895 761088 023187 806366 843526 822304 207038 229774 965341 391993 868287 805707 144265 736310 541979 895659 471553 898900 164981 093402 892477 667139 911680 / 667918 064713 759191 716264 959348 964354 823018 255175 218124 976008 103563 477224 395879 > 1694 [i]