Information on Result #1707834
Digital (51, 57, 4782984)-net over F3, using net defined by OOA based on linear OOA(357, 4782984, F3, 6, 6) (dual of [(4782984, 6), 28697847, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(357, 4782984, F3, 5, 6) (dual of [(4782984, 5), 23914863, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(357, 4782984, F3, 6) (dual of [4782984, 4782927, 7]-code), using
- 1 times truncation [i] based on linear OA(358, 4782985, F3, 7) (dual of [4782985, 4782927, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(357, 4782969, F3, 7) (dual of [4782969, 4782912, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- 1 times truncation [i] based on linear OA(358, 4782985, F3, 7) (dual of [4782985, 4782927, 8]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(357, 4782984, F3, 6) (dual of [4782984, 4782927, 7]-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.