Best Known (108−100, 108, s)-Nets in Base 16
(108−100, 108, 65)-Net over F16 — Constructive and digital
Digital (8, 108, 65)-net over F16, using
- t-expansion [i] based on digital (6, 108, 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
(108−100, 108, 217)-Net in Base 16 — Upper bound on s
There is no (8, 108, 218)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16108, 218, S16, 100), but
- the linear programming bound shows that M ≥ 28529 825500 289957 056568 690012 244623 123307 994611 716271 712718 078086 718391 445099 028263 362338 987007 077920 346957 992782 556135 895722 558466 686709 790560 049847 916840 122963 254268 005532 354745 302980 464772 186404 462477 128972 841477 210112 / 2 513061 169472 144177 006586 075356 612019 013999 285592 421382 464934 332381 367989 344583 313029 699677 > 16108 [i]