Best Known (174−24, 174, s)-Nets in Base 4
(174−24, 174, 21850)-Net over F4 — Constructive and digital
Digital (150, 174, 21850)-net over F4, using
- net defined by OOA [i] based on linear OOA(4174, 21850, F4, 24, 24) (dual of [(21850, 24), 524226, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4174, 262200, F4, 24) (dual of [262200, 262026, 25]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4173, 262199, F4, 24) (dual of [262199, 262026, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4118, 262144, F4, 18) (dual of [262144, 262026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(410, 55, F4, 5) (dual of [55, 45, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4173, 262199, F4, 24) (dual of [262199, 262026, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(4174, 262200, F4, 24) (dual of [262200, 262026, 25]-code), using
(174−24, 174, 163707)-Net over F4 — Digital
Digital (150, 174, 163707)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4174, 163707, F4, 24) (dual of [163707, 163533, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4174, 262200, F4, 24) (dual of [262200, 262026, 25]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4173, 262199, F4, 24) (dual of [262199, 262026, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4118, 262144, F4, 18) (dual of [262144, 262026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(410, 55, F4, 5) (dual of [55, 45, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4173, 262199, F4, 24) (dual of [262199, 262026, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4174, 262200, F4, 24) (dual of [262200, 262026, 25]-code), using
(174−24, 174, large)-Net in Base 4 — Upper bound on s
There is no (150, 174, large)-net in base 4, because
- 22 times m-reduction [i] would yield (150, 152, large)-net in base 4, but