Best Known (15, 32, s)-Nets in Base 49
(15, 32, 152)-Net over F49 — Constructive and digital
Digital (15, 32, 152)-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 (1, 9, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (1, 18, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49 (see above)
- digital (0, 5, 50)-net over F49, using
(15, 32, 410)-Net over F49 — Digital
Digital (15, 32, 410)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4932, 410, F49, 17) (dual of [410, 378, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4932, 481, F49, 17) (dual of [481, 449, 18]-code), using
- an extension Ce(16) of the narrow-sense BCH-code C(I) with length 480 | 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(4932, 481, F49, 17) (dual of [481, 449, 18]-code), using
(15, 32, 277941)-Net in Base 49 — Upper bound on s
There is no (15, 32, 277942)-net in base 49, because
- 1 times m-reduction [i] would yield (15, 31, 277942)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 24893 653236 911494 010194 691650 951700 805542 171636 882689 > 4931 [i]