Information on Result #1761073
Digital (57, 73, 1098)-net over F3, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(373, 1098, F3, 2, 16) (dual of [(1098, 2), 2123, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(373, 2196, F3, 16) (dual of [2196, 2123, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(373, 2197, F3, 16) (dual of [2197, 2124, 17]-code), using
- construction XX applied to Ce(15) ⊂ Ce(13) ⊂ Ce(12) [i] based on
- linear OA(371, 2187, F3, 16) (dual of [2187, 2116, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(364, 2187, F3, 14) (dual of [2187, 2123, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(357, 2187, F3, 13) (dual of [2187, 2130, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(31, 9, F3, 1) (dual of [9, 8, 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
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(15) ⊂ Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(373, 2197, F3, 16) (dual of [2197, 2124, 17]-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.