Best Known (12, 12+16, s)-Nets in Base 49
(12, 12+16, 104)-Net over F49 — Constructive and digital
Digital (12, 28, 104)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49, using
- digital (2, 18, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49 (see above)
- digital (2, 10, 52)-net over F49, using
(12, 12+16, 223)-Net over F49 — Digital
Digital (12, 28, 223)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4928, 223, F49, 16) (dual of [223, 195, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4928, 240, F49, 16) (dual of [240, 212, 17]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 240 | 492−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(4928, 240, F49, 16) (dual of [240, 212, 17]-code), using
(12, 12+16, 64581)-Net in Base 49 — Upper bound on s
There is no (12, 28, 64582)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 211591 660805 635874 411809 355765 093878 103614 199041 > 4928 [i]