Best Known (11, 15, s)-Nets in Base 49
(11, 15, 2882452)-Net over F49 — Constructive and digital
Digital (11, 15, 2882452)-net over F49, using
- net defined by OOA [i] based on linear OOA(4915, 2882452, F49, 4, 4) (dual of [(2882452, 4), 11529793, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(4915, 2882452, F49, 3, 4) (dual of [(2882452, 3), 8647341, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(492, 50, F49, 3, 2) (dual of [(50, 3), 148, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;148,49) [i]
- linear OOA(4913, 2882402, F49, 3, 4) (dual of [(2882402, 3), 8647193, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(499, 5764801, F49, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 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 Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), using
- linear OOA(492, 50, F49, 3, 2) (dual of [(50, 3), 148, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(4915, 2882452, F49, 3, 4) (dual of [(2882452, 3), 8647341, 5]-NRT-code), using
(11, 15, large)-Net over F49 — Digital
Digital (11, 15, large)-net over F49, using
- net defined by OOA [i] based on linear OOA(4915, large, F49, 4, 4), using
- appending kth column [i] based on linear OOA(4915, large, F49, 3, 4), using
(11, 15, large)-Net in Base 49 — Upper bound on s
There is no (11, 15, large)-net in base 49, because
- 2 times m-reduction [i] would yield (11, 13, large)-net in base 49, but