Information on Result #1840089
(36, 41, 524298)-net in base 2, using net defined by OOA based on OOA(241, 524298, S2, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(241, 1048597, S2, 5), using
- construction X4 applied to RM(1,20) ⊂ K(20) [i] based on
- OA(240, 1048576, S2, 5), using Kerdock OA K(20) [i]
- linear OA(221, 1048576, F2, 3) (dual of [1048576, 1048555, 4]-code or 1048576-cap in PG(20,2)), using Reed–Muller code RM(1,20) [i]
- linear OA(220, 21, F2, 19) (dual of [21, 1, 20]-code), using
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- dual of repetition code with length 21 [i]
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- linear OA(21, 21, F2, 1) (dual of [21, 20, 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 RM(1,20) ⊂ K(20) [i] based on
Mode: Constructive.
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 | (170, 180, 4718599)-net in base 2 | [i] | (u, u+v)-Construction for Nets | |
| 2 | (170, 181, 4718599)-net in base 2 | [i] | ||