Best Known (20−11, 20, s)-Nets in Base 49
(20−11, 20, 151)-Net over F49 — Constructive and digital
Digital (9, 20, 151)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 3, 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, 5, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (1, 12, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 3, 50)-net over F49, using
(20−11, 20, 316)-Net over F49 — Digital
Digital (9, 20, 316)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4920, 316, F49, 11) (dual of [316, 296, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(4920, 480, F49, 11) (dual of [480, 460, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 480 | 492−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(4920, 480, F49, 11) (dual of [480, 460, 12]-code), using
(20−11, 20, 143659)-Net in Base 49 — Upper bound on s
There is no (9, 20, 143660)-net in base 49, because
- 1 times m-reduction [i] would yield (9, 19, 143660)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 129 937963 603335 705592 278181 651777 > 4919 [i]