Information on Result #1840090
(40, 45, 2097163)-net in base 2, using net defined by OOA based on OOA(245, 2097163, S2, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(245, 4194327, S2, 5), using
- construction X4 applied to RM(1,22) ⊂ K(22) [i] based on
- OA(244, 4194304, S2, 5), using Kerdock OA K(22) [i]
- linear OA(223, 4194304, F2, 3) (dual of [4194304, 4194281, 4]-code or 4194304-cap in PG(22,2)), using Reed–Muller code RM(1,22) [i]
- linear OA(222, 23, F2, 21) (dual of [23, 1, 22]-code), using
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- dual of repetition code with length 23 [i]
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- linear OA(21, 23, F2, 1) (dual of [23, 22, 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(1,22) ⊂ K(22) [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 | (174, 184, 6291464)-net in base 2 | [i] | (u, u+v)-Construction for Nets | |
| 2 | (174, 185, 6291464)-net in base 2 | [i] | ||