Best Known (86−73, 86, s)-Nets in Base 8
(86−73, 86, 48)-Net over F8 — Constructive and digital
Digital (13, 86, 48)-net over F8, using
- t-expansion [i] based on digital (11, 86, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
(86−73, 86, 56)-Net over F8 — Digital
Digital (13, 86, 56)-net over F8, using
- net from sequence [i] based on digital (13, 55)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 13 and N(F) ≥ 56, using
(86−73, 86, 235)-Net over F8 — Upper bound on s (digital)
There is no digital (13, 86, 236)-net over F8, because
- 1 times m-reduction [i] would yield digital (13, 85, 236)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(885, 236, F8, 72) (dual of [236, 151, 73]-code), but
- residual code [i] would yield OA(813, 163, S8, 9), but
- 1 times truncation [i] would yield OA(812, 162, S8, 8), but
- the linear programming bound shows that M ≥ 12 319920 743776 256000 / 177 696713 > 812 [i]
- 1 times truncation [i] would yield OA(812, 162, S8, 8), but
- residual code [i] would yield OA(813, 163, S8, 9), but
- extracting embedded orthogonal array [i] would yield linear OA(885, 236, F8, 72) (dual of [236, 151, 73]-code), but
(86−73, 86, 241)-Net in Base 8 — Upper bound on s
There is no (13, 86, 242)-net in base 8, because
- 22 times m-reduction [i] would yield (13, 64, 242)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(864, 242, S8, 51), but
- the linear programming bound shows that M ≥ 70 232740 660466 146387 371112 364270 550714 612400 798807 017251 810317 649288 784222 788532 961057 620751 780826 891846 178327 052743 502456 032729 337117 589164 303319 040000 / 10982 962511 522080 424097 485508 217442 568541 585265 006918 081487 297620 694440 959423 507493 470379 310181 > 864 [i]
- extracting embedded orthogonal array [i] would yield OA(864, 242, S8, 51), but