Best Known (10, 10+15, s)-Nets in Base 49
(10, 10+15, 103)-Net over F49 — Constructive and digital
Digital (10, 25, 103)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (2, 17, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49, using
- digital (1, 8, 51)-net over F49, using
(10, 10+15, 151)-Net over F49 — Digital
Digital (10, 25, 151)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4925, 151, F49, 15) (dual of [151, 126, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4925, 152, F49, 15) (dual of [152, 127, 16]-code), using
- construction X applied to C([17,31]) ⊂ C([18,31]) [i] based on
- linear OA(4925, 150, F49, 15) (dual of [150, 125, 16]-code), using the BCH-code C(I) with length 150 | 492−1, defining interval I = {17,18,…,31}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(4923, 150, F49, 14) (dual of [150, 127, 15]-code), using the BCH-code C(I) with length 150 | 492−1, defining interval I = {18,19,…,31}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to C([17,31]) ⊂ C([18,31]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4925, 152, F49, 15) (dual of [152, 127, 16]-code), using
(10, 10+15, 43914)-Net in Base 49 — Upper bound on s
There is no (10, 25, 43915)-net in base 49, because
- 1 times m-reduction [i] would yield (10, 24, 43915)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 36708 454204 297878 725925 625156 609228 931185 > 4924 [i]