Information on Result #1707590
Digital (18, 23, 2197)-net over F3, using net defined by OOA based on linear OOA(323, 2197, F3, 5, 5) (dual of [(2197, 5), 10962, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(323, 2197, F3, 4, 5) (dual of [(2197, 4), 8765, 6]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(323, 2197, F3, 5) (dual of [2197, 2174, 6]-code), using
- 2 step Varšamov–Edel lengthening with (ri) = (1, 0) [i] based on linear OA(322, 2194, F3, 5) (dual of [2194, 2172, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(322, 2187, F3, 5) (dual of [2187, 2165, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(315, 2187, F3, 4) (dual of [2187, 2172, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 7, F3, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- 2 step Varšamov–Edel lengthening with (ri) = (1, 0) [i] based on linear OA(322, 2194, F3, 5) (dual of [2194, 2172, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(323, 2197, F3, 5) (dual of [2197, 2174, 6]-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.