Best Known (14, 14+16, s)-Nets in Base 49
(14, 14+16, 151)-Net over F49 — Constructive and digital
Digital (14, 30, 151)-net over F49, using
- 1 times m-reduction [i] based on digital (14, 31, 151)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 5, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- digital (0, 8, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (1, 18, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 5, 50)-net over F49, using
- generalized (u, u+v)-construction [i] based on
(14, 14+16, 393)-Net over F49 — Digital
Digital (14, 30, 393)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4930, 393, F49, 16) (dual of [393, 363, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4930, 480, F49, 16) (dual of [480, 450, 17]-code), using
(14, 14+16, 170873)-Net in Base 49 — Upper bound on s
There is no (14, 30, 170874)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 508 032874 341489 048942 577259 629748 537092 032303 004417 > 4930 [i]