Best Known (173, 202, s)-Nets in Base 4
(173, 202, 18727)-Net over F4 — Constructive and digital
Digital (173, 202, 18727)-net over F4, using
- 44 times duplication [i] based on digital (169, 198, 18727)-net over F4, using
- net defined by OOA [i] based on linear OOA(4198, 18727, F4, 29, 29) (dual of [(18727, 29), 542885, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4198, 262179, F4, 29) (dual of [262179, 261981, 30]-code), using
- 3 times code embedding in larger space [i] based on linear OA(4195, 262176, F4, 29) (dual of [262176, 261981, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(4195, 262176, F4, 29) (dual of [262176, 261981, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4198, 262179, F4, 29) (dual of [262179, 261981, 30]-code), using
- net defined by OOA [i] based on linear OOA(4198, 18727, F4, 29, 29) (dual of [(18727, 29), 542885, 30]-NRT-code), using
(173, 202, 131096)-Net over F4 — Digital
Digital (173, 202, 131096)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4202, 131096, F4, 2, 29) (dual of [(131096, 2), 261990, 30]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4200, 131095, F4, 2, 29) (dual of [(131095, 2), 261990, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4200, 262190, F4, 29) (dual of [262190, 261990, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4154, 262144, F4, 23) (dual of [262144, 261990, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(410, 46, F4, 5) (dual of [46, 36, 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(28) ⊂ Ce(22) [i] based on
- OOA 2-folding [i] based on linear OA(4200, 262190, F4, 29) (dual of [262190, 261990, 30]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4200, 131095, F4, 2, 29) (dual of [(131095, 2), 261990, 30]-NRT-code), using
(173, 202, large)-Net in Base 4 — Upper bound on s
There is no (173, 202, large)-net in base 4, because
- 27 times m-reduction [i] would yield (173, 175, large)-net in base 4, but