Information on Result #1179156
Digital (37, 46, 515)-net over F2, using net defined by OOA based on linear OOA(246, 515, F2, 9, 9) (dual of [(515, 9), 4589, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(246, 515, F2, 8, 9) (dual of [(515, 8), 4074, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(246, 2061, F2, 9) (dual of [2061, 2015, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(245, 2048, F2, 9) (dual of [2048, 2003, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(234, 2048, F2, 7) (dual of [2048, 2014, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(212, 13, F2, 11) (dual of [13, 1, 12]-code), using
- strength reduction [i] based on linear OA(212, 13, F2, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
- dual of repetition code with length 13 [i]
- strength reduction [i] based on linear OA(212, 13, F2, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
- linear OA(21, 13, F2, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(246, 2061, F2, 9) (dual of [2061, 2015, 10]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (38, 46, 515)-net over F2 | [i] | t-Expansion | |
| 2 | Digital (38, 47, 515)-net over F2 | [i] | Net Duplication | |
| 3 | Digital (39, 48, 515)-net over F2 | [i] | ||
| 4 | Digital (235, 253, 932582)-net over F2 | [i] | (u, u+v)-Construction for Nets | |
| 5 | Digital (235, 254, 932581)-net over F2 | [i] | ||