Information on Result #1744368
Digital (30, 51, 1351)-net over F64, using net defined by OOA based on linear OOA(6451, 1351, F64, 27, 21) (dual of [(1351, 27), 36426, 22]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(6451, 5405, F64, 3, 21) (dual of [(5405, 3), 16164, 22]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6451, 5405, F64, 21) (dual of [5405, 5354, 22]-code), using
- 1297 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 4 times 0, 1, 16 times 0, 1, 49 times 0, 1, 137 times 0, 1, 348 times 0, 1, 735 times 0) [i] based on linear OA(6441, 4098, F64, 21) (dual of [4098, 4057, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(6441, 4096, F64, 21) (dual of [4096, 4055, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- 1297 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 4 times 0, 1, 16 times 0, 1, 49 times 0, 1, 137 times 0, 1, 348 times 0, 1, 735 times 0) [i] based on linear OA(6441, 4098, F64, 21) (dual of [4098, 4057, 22]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6451, 5405, F64, 21) (dual of [5405, 5354, 22]-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.