Best Known (17, 17+20, s)-Nets in Base 49
(17, 17+20, 151)-Net over F49 — Constructive and digital
Digital (17, 37, 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, 10, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (1, 21, 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
(17, 17+20, 370)-Net over F49 — Digital
Digital (17, 37, 370)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4937, 370, F49, 20) (dual of [370, 333, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4937, 400, F49, 20) (dual of [400, 363, 21]-code), using
(17, 17+20, 169218)-Net in Base 49 — Upper bound on s
There is no (17, 37, 169219)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 344 557270 736318 267237 946831 078397 432181 498277 555557 704459 576225 > 4937 [i]