Best Known (147−13, 147, s)-Nets in Base 4
(147−13, 147, 4194301)-Net over F4 — Constructive and digital
Digital (134, 147, 4194301)-net over F4, using
- net defined by OOA [i] based on linear OOA(4147, 4194301, F4, 15, 13) (dual of [(4194301, 15), 62914368, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(4147, large, F4, 3, 13), using
- trace code [i] based on linear OOA(6449, 2796201, F64, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
- trace code [i] based on linear OOA(6449, 2796201, F64, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(4147, large, F4, 3, 13), using
(147−13, 147, large)-Net over F4 — Digital
Digital (134, 147, large)-net over F4, using
- 42 times duplication [i] based on digital (132, 145, large)-net over F4, using
- t-expansion [i] based on digital (130, 145, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4145, large, F4, 15) (dual of [large, large−145, 16]-code), using
- strength reduction [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- strength reduction [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4145, large, F4, 15) (dual of [large, large−145, 16]-code), using
- t-expansion [i] based on digital (130, 145, large)-net over F4, using
(147−13, 147, large)-Net in Base 4 — Upper bound on s
There is no (134, 147, large)-net in base 4, because
- 11 times m-reduction [i] would yield (134, 136, large)-net in base 4, but