Best Known (17, 17+28, s)-Nets in Base 3
(17, 17+28, 28)-Net over F3 — Constructive and digital
Digital (17, 45, 28)-net over F3, using
- t-expansion [i] based on digital (15, 45, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
(17, 17+28, 90)-Net in Base 3 — Upper bound on s
There is no (17, 45, 91)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3172 095414 014279 591997 > 345 [i]
- extracting embedded orthogonal array [i] would yield OA(345, 91, S3, 28), but
- the linear programming bound shows that M ≥ 81 327158 238838 159088 201290 238235 431762 159166 500178 228192 584061 622908 772686 005688 353801 809230 048052 104203 312176 776912 121525 227901 623974 672880 / 26999 517132 094337 869327 753678 825108 185384 506812 305552 784668 595120 416177 250179 677458 156350 472125 757223 702933 491485 850369 > 345 [i]