Best Known (144−28, 144, s)-Nets in Base 5
(144−28, 144, 1119)-Net over F5 — Constructive and digital
Digital (116, 144, 1119)-net over F5, using
- net defined by OOA [i] based on linear OOA(5144, 1119, F5, 28, 28) (dual of [(1119, 28), 31188, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(5144, 15666, F5, 28) (dual of [15666, 15522, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(5144, 15670, F5, 28) (dual of [15670, 15526, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- linear OA(5133, 15625, F5, 28) (dual of [15625, 15492, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(511, 45, F5, 6) (dual of [45, 34, 7]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(5144, 15670, F5, 28) (dual of [15670, 15526, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(5144, 15666, F5, 28) (dual of [15666, 15522, 29]-code), using
(144−28, 144, 15670)-Net over F5 — Digital
Digital (116, 144, 15670)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5144, 15670, F5, 28) (dual of [15670, 15526, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- linear OA(5133, 15625, F5, 28) (dual of [15625, 15492, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(511, 45, F5, 6) (dual of [45, 34, 7]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
(144−28, 144, large)-Net in Base 5 — Upper bound on s
There is no (116, 144, large)-net in base 5, because
- 26 times m-reduction [i] would yield (116, 118, large)-net in base 5, but