Best Known (133−9, 133, s)-Nets in Base 8
(133−9, 133, large)-Net over F8 — Constructive and digital
Digital (124, 133, large)-net over F8, using
- 2 times m-reduction [i] based on digital (124, 135, large)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (119, 130, 8388602)-net over F8, using
- trace code for nets [i] based on digital (54, 65, 4194301)-net over F64, using
- net defined by OOA [i] based on linear OOA(6465, 4194301, F64, 15, 11) (dual of [(4194301, 15), 62914450, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6465, large, F64, 3, 11), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(647, 2796201, F64, 3, 3) (dual of [(2796201, 3), 8388596, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(647, 8388602, F64, 3, 3) (dual of [(8388602, 3), 25165799, 4]-NRT-code), using
- OOA stacking with additional row [i] based on linear OA(647, large, F64, 3) (dual of [large, large−7, 4]-code), using
- discarding factors / shortening the dual code based on linear OOA(647, 8388602, F64, 3, 3) (dual of [(8388602, 3), 25165799, 4]-NRT-code), using
- linear OOA(6417, 2796201, F64, 3, 5) (dual of [(2796201, 3), 8388586, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6417, 4194301, F64, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(6417, large, F64, 5) (dual of [large, large−17, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(6417, large, F64, 5) (dual of [large, large−17, 6]-code), using
- discarding factors / shortening the dual code based on linear OOA(6417, 4194301, F64, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- linear OOA(6441, 2796201, F64, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- linear OOA(647, 2796201, F64, 3, 3) (dual of [(2796201, 3), 8388596, 4]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6465, large, F64, 3, 11), using
- net defined by OOA [i] based on linear OOA(6465, 4194301, F64, 15, 11) (dual of [(4194301, 15), 62914450, 12]-NRT-code), using
- trace code for nets [i] based on digital (54, 65, 4194301)-net over F64, using
- digital (0, 5, 9)-net over F8, using
- (u, u+v)-construction [i] based on
(133−9, 133, large)-Net in Base 8 — Upper bound on s
There is no (124, 133, large)-net in base 8, because
- 7 times m-reduction [i] would yield (124, 126, large)-net in base 8, but