Best Known (119−24, 119, s)-Nets in Base 5
(119−24, 119, 1303)-Net over F5 — Constructive and digital
Digital (95, 119, 1303)-net over F5, using
- 53 times duplication [i] based on digital (92, 116, 1303)-net over F5, using
- net defined by OOA [i] based on linear OOA(5116, 1303, F5, 24, 24) (dual of [(1303, 24), 31156, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(5116, 15636, F5, 24) (dual of [15636, 15520, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5116, 15638, F5, 24) (dual of [15638, 15522, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(5103, 15625, F5, 22) (dual of [15625, 15522, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(51, 13, F5, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(5116, 15638, F5, 24) (dual of [15638, 15522, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(5116, 15636, F5, 24) (dual of [15636, 15520, 25]-code), using
- net defined by OOA [i] based on linear OOA(5116, 1303, F5, 24, 24) (dual of [(1303, 24), 31156, 25]-NRT-code), using
(119−24, 119, 12685)-Net over F5 — Digital
Digital (95, 119, 12685)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5119, 12685, F5, 24) (dual of [12685, 12566, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5119, 15647, F5, 24) (dual of [15647, 15528, 25]-code), using
- 1 times code embedding in larger space [i] based on linear OA(5118, 15646, F5, 24) (dual of [15646, 15528, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(53, 21, F5, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(5118, 15646, F5, 24) (dual of [15646, 15528, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5119, 15647, F5, 24) (dual of [15647, 15528, 25]-code), using
(119−24, 119, large)-Net in Base 5 — Upper bound on s
There is no (95, 119, large)-net in base 5, because
- 22 times m-reduction [i] would yield (95, 97, large)-net in base 5, but