Best Known (62−52, 62, s)-Nets in Base 8
(62−52, 62, 46)-Net over F8 — Constructive and digital
Digital (10, 62, 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]
(62−52, 62, 159)-Net in Base 8 — Upper bound on s
There is no (10, 62, 160)-net in base 8, because
- 1 times m-reduction [i] would yield (10, 61, 160)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(861, 160, S8, 51), but
- the linear programming bound shows that M ≥ 916491 456803 806802 853724 385858 544072 708829 910119 602304 314993 512489 449409 636013 036497 080897 583782 743579 470627 903160 006308 701772 185600 / 72844 197799 691985 895636 947018 611948 215650 842034 313217 872209 962216 415617 544543 > 861 [i]
- extracting embedded orthogonal array [i] would yield OA(861, 160, S8, 51), but