Best Known (68−58, 68, s)-Nets in Base 8
(68−58, 68, 46)-Net over F8 — Constructive and digital
Digital (10, 68, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
(68−58, 68, 128)-Net in Base 8 — Upper bound on s
There is no (10, 68, 129)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(868, 129, S8, 58), but
- the linear programming bound shows that M ≥ 20 423916 642337 205523 928607 099756 711293 246644 779949 302711 254567 876669 357102 726545 532958 919416 099938 071027 095965 862225 974464 449597 862840 382815 334612 368701 259776 / 792164 797992 276600 764564 676858 309110 181230 101805 412678 737259 727537 315744 123907 878278 981123 447823 > 868 [i]