Best Known (34−18, 34, s)-Nets in Base 49
(34−18, 34, 151)-Net over F49 — Constructive and digital
Digital (16, 34, 151)-net over F49, using
- 1 times m-reduction [i] based on digital (16, 35, 151)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 6, 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, 9, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (1, 20, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 6, 50)-net over F49, using
- generalized (u, u+v)-construction [i] based on
(34−18, 34, 427)-Net over F49 — Digital
Digital (16, 34, 427)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4934, 427, F49, 18) (dual of [427, 393, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4934, 481, F49, 18) (dual of [481, 447, 19]-code), using
- an extension Ce(17) of the narrow-sense BCH-code C(I) with length 480 | 492−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(4934, 481, F49, 18) (dual of [481, 447, 19]-code), using
(34−18, 34, 209742)-Net in Base 49 — Upper bound on s
There is no (16, 34, 209743)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 2928 690091 644147 722659 206302 330354 214015 937385 298329 466193 > 4934 [i]