Best Known (10, 24, s)-Nets in Base 49
(10, 24, 103)-Net over F49 — Constructive and digital
Digital (10, 24, 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, 16, 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, 24, 166)-Net over F49 — Digital
Digital (10, 24, 166)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4924, 166, F49, 14) (dual of [166, 142, 15]-code), using
- 13 step Varšamov–Edel lengthening with (ri) = (1, 12 times 0) [i] based on linear OA(4923, 152, F49, 14) (dual of [152, 129, 15]-code), using
- construction X applied to C([18,31]) ⊂ C([19,31]) [i] based on
- 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(4921, 150, F49, 13) (dual of [150, 129, 14]-code), using the BCH-code C(I) with length 150 | 492−1, defining interval I = {19,20,…,31}, and designed minimum distance d ≥ |I|+1 = 14 [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([18,31]) ⊂ C([19,31]) [i] based on
- 13 step Varšamov–Edel lengthening with (ri) = (1, 12 times 0) [i] based on linear OA(4923, 152, F49, 14) (dual of [152, 129, 15]-code), using
(10, 24, 43914)-Net in Base 49 — Upper bound on s
There is no (10, 24, 43915)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 36708 454204 297878 725925 625156 609228 931185 > 4924 [i]