Information on Result #1230136
Digital (111, 123, large)-net over F16, using generalized (u, u+v)-construction based on
- digital (0, 2, 17)-net over F16, using
- digital (0, 3, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (15, 19, 2796200)-net over F16, using
- s-reduction based on digital (15, 19, 4194301)-net over F16, using
- net defined by OOA [i] based on linear OOA(1619, 4194301, F16, 4, 4) (dual of [(4194301, 4), 16777185, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(1619, 8388602, F16, 4) (dual of [8388602, 8388583, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(1619, large, F16, 4) (dual of [large, large−19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(1619, large, F16, 4) (dual of [large, large−19, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(1619, 8388602, F16, 4) (dual of [8388602, 8388583, 5]-code), using
- net defined by OOA [i] based on linear OOA(1619, 4194301, F16, 4, 4) (dual of [(4194301, 4), 16777185, 5]-NRT-code), using
- s-reduction based on digital (15, 19, 4194301)-net over F16, using
- digital (25, 31, 2796200)-net over F16, using
- s-reduction based on digital (25, 31, 2796201)-net over F16, using
- net defined by OOA [i] based on linear OOA(1631, 2796201, F16, 6, 6) (dual of [(2796201, 6), 16777175, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(1631, large, F16, 6) (dual of [large, large−31, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(1631, large, F16, 6) (dual of [large, large−31, 7]-code), using
- net defined by OOA [i] based on linear OOA(1631, 2796201, F16, 6, 6) (dual of [(2796201, 6), 16777175, 7]-NRT-code), using
- s-reduction based on digital (25, 31, 2796201)-net over F16, using
- digital (56, 68, 2796200)-net over F16, using
- net defined by OOA [i] based on linear OOA(1668, 2796200, F16, 14, 12) (dual of [(2796200, 14), 39146732, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(1668, 8388601, F16, 2, 12) (dual of [(8388601, 2), 16777134, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1668, 8388602, F16, 2, 12) (dual of [(8388602, 2), 16777136, 13]-NRT-code), using
- trace code [i] based on linear OOA(25634, 4194301, F256, 2, 12) (dual of [(4194301, 2), 8388568, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25634, 8388602, F256, 12) (dual of [8388602, 8388568, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- OOA 2-folding [i] based on linear OA(25634, 8388602, F256, 12) (dual of [8388602, 8388568, 13]-code), using
- trace code [i] based on linear OOA(25634, 4194301, F256, 2, 12) (dual of [(4194301, 2), 8388568, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1668, 8388602, F16, 2, 12) (dual of [(8388602, 2), 16777136, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(1668, 8388601, F16, 2, 12) (dual of [(8388601, 2), 16777134, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1668, 2796200, F16, 14, 12) (dual of [(2796200, 14), 39146732, 13]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (112, 123, large)-net over F16 | [i] | t-Expansion | |
| 2 | Digital (112, 124, large)-net over F16 | [i] | Net Duplication | |
| 3 | Digital (111, 122, large)-net over F16 | [i] | m-Reduction | |
| 4 | Digital (111, 121, large)-net over F16 | [i] | ||
| 5 | Digital (111, 120, large)-net over F16 | [i] | ||
| 6 | Digital (111, 119, large)-net over F16 | [i] | ||
| 7 | Digital (111, 118, large)-net over F16 | [i] | ||
| 8 | Digital (111, 117, large)-net over F16 | [i] | ||
| 9 | Digital (111, 116, large)-net over F16 | [i] | ||
| 10 | Digital (111, 115, large)-net over F16 | [i] | ||
| 11 | Digital (111, 114, large)-net over F16 | [i] | ||