Best Known (115−98, 115, s)-Nets in Base 8
(115−98, 115, 65)-Net over F8 — Constructive and digital
Digital (17, 115, 65)-net over F8, using
- t-expansion [i] based on digital (14, 115, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(115−98, 115, 146)-Net in Base 8 — Upper bound on s
There is no (17, 115, 147)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(8115, 147, S8, 98), but
- the linear programming bound shows that M ≥ 599345 416299 388973 235507 022177 177118 046850 911577 140306 689015 460811 889080 427692 784047 046445 821063 607212 795117 279723 192210 808892 966020 579328 / 7743 507384 508665 125912 260586 578125 > 8115 [i]