Information on Result #1744448
Digital (31, 53, 1277)-net over F64, using net defined by OOA based on linear OOA(6453, 1277, F64, 27, 22) (dual of [(1277, 27), 34426, 23]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(6453, 5109, F64, 3, 22) (dual of [(5109, 3), 15274, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6453, 5110, F64, 3, 22) (dual of [(5110, 3), 15277, 23]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6453, 5110, F64, 22) (dual of [5110, 5057, 23]-code), using
- 1000 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 0, 1, 11 times 0, 1, 35 times 0, 1, 99 times 0, 1, 261 times 0, 1, 585 times 0) [i] based on linear OA(6444, 4101, F64, 22) (dual of [4101, 4057, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6439, 4096, F64, 20) (dual of [4096, 4057, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- 1000 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 0, 1, 11 times 0, 1, 35 times 0, 1, 99 times 0, 1, 261 times 0, 1, 585 times 0) [i] based on linear OA(6444, 4101, F64, 22) (dual of [4101, 4057, 23]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6453, 5110, F64, 22) (dual of [5110, 5057, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(6453, 5110, F64, 3, 22) (dual of [(5110, 3), 15277, 23]-NRT-code), using
Mode: 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
None.