Information on Result #1743266
Digital (27, 41, 19609)-net over F49, using net defined by OOA based on linear OOA(4941, 19609, F49, 21, 14) (dual of [(19609, 21), 411748, 15]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(4941, 58828, F49, 3, 14) (dual of [(58828, 3), 176443, 15]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4941, 58828, F49, 2, 14) (dual of [(58828, 2), 117615, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4941, 117656, F49, 14) (dual of [117656, 117615, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(4940, 117649, F49, 14) (dual of [117649, 117609, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- OOA 2-folding [i] based on linear OA(4941, 117656, F49, 14) (dual of [117656, 117615, 15]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4941, 58828, F49, 2, 14) (dual of [(58828, 2), 117615, 15]-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.