Best Known (150−29, 150, s)-Nets in Base 5
(150−29, 150, 1119)-Net over F5 — Constructive and digital
Digital (121, 150, 1119)-net over F5, using
- net defined by OOA [i] based on linear OOA(5150, 1119, F5, 29, 29) (dual of [(1119, 29), 32301, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(5150, 15667, F5, 29) (dual of [15667, 15517, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(5150, 15670, F5, 29) (dual of [15670, 15520, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(5139, 15625, F5, 29) (dual of [15625, 15486, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(511, 45, F5, 6) (dual of [45, 34, 7]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(5150, 15670, F5, 29) (dual of [15670, 15520, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(5150, 15667, F5, 29) (dual of [15667, 15517, 30]-code), using
(150−29, 150, 15697)-Net over F5 — Digital
Digital (121, 150, 15697)-net over F5, using
(150−29, 150, large)-Net in Base 5 — Upper bound on s
There is no (121, 150, large)-net in base 5, because
- 27 times m-reduction [i] would yield (121, 123, large)-net in base 5, but