Best Known (6, 15, s)-Nets in Base 49
(6, 15, 102)-Net over F49 — Constructive and digital
Digital (6, 15, 102)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (1, 10, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49 (see above)
- digital (1, 5, 51)-net over F49, using
(6, 15, 167)-Net over F49 — Digital
Digital (6, 15, 167)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4915, 167, F49, 9) (dual of [167, 152, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(4915, 200, F49, 9) (dual of [200, 185, 10]-code), using
(6, 15, 37973)-Net in Base 49 — Upper bound on s
There is no (6, 15, 37974)-net in base 49, because
- 1 times m-reduction [i] would yield (6, 14, 37974)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 460014 500419 591736 942209 > 4914 [i]