Best Known (147, 171, s)-Nets in Base 4
(147, 171, 21849)-Net over F4 — Constructive and digital
Digital (147, 171, 21849)-net over F4, using
- 41 times duplication [i] based on digital (146, 170, 21849)-net over F4, using
- net defined by OOA [i] based on linear OOA(4170, 21849, F4, 24, 24) (dual of [(21849, 24), 524206, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4170, 262188, F4, 24) (dual of [262188, 262018, 25]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(4163, 262145, F4, 25) (dual of [262145, 261982, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(4127, 262145, F4, 19) (dual of [262145, 262018, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- OA 12-folding and stacking [i] based on linear OA(4170, 262188, F4, 24) (dual of [262188, 262018, 25]-code), using
- net defined by OOA [i] based on linear OOA(4170, 21849, F4, 24, 24) (dual of [(21849, 24), 524206, 25]-NRT-code), using
(147, 171, 135506)-Net over F4 — Digital
Digital (147, 171, 135506)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4171, 135506, F4, 24) (dual of [135506, 135335, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4171, 262189, F4, 24) (dual of [262189, 262018, 25]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4170, 262188, F4, 24) (dual of [262188, 262018, 25]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(4163, 262145, F4, 25) (dual of [262145, 261982, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(4127, 262145, F4, 19) (dual of [262145, 262018, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4170, 262188, F4, 24) (dual of [262188, 262018, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4171, 262189, F4, 24) (dual of [262189, 262018, 25]-code), using
(147, 171, large)-Net in Base 4 — Upper bound on s
There is no (147, 171, large)-net in base 4, because
- 22 times m-reduction [i] would yield (147, 149, large)-net in base 4, but