Information on Result #1716672
Digital (189, 223, 4741)-net over F3, using net defined by OOA based on linear OOA(3223, 4741, F3, 45, 34) (dual of [(4741, 45), 213122, 35]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(3223, 18965, F3, 5, 34) (dual of [(18965, 5), 94602, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3223, 18966, F3, 5, 34) (dual of [(18966, 5), 94607, 35]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3223, 18966, F3, 3, 34) (dual of [(18966, 3), 56675, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3223, 19687, F3, 3, 34) (dual of [(19687, 3), 58838, 35]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3223, 59061, F3, 34) (dual of [59061, 58838, 35]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3222, 59060, F3, 34) (dual of [59060, 58838, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(31) [i] based on
- linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3211, 59049, F3, 32) (dual of [59049, 58838, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 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 X applied to Ce(33) ⊂ Ce(31) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3222, 59060, F3, 34) (dual of [59060, 58838, 35]-code), using
- OOA 3-folding [i] based on linear OA(3223, 59061, F3, 34) (dual of [59061, 58838, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(3223, 19687, F3, 3, 34) (dual of [(19687, 3), 58838, 35]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3223, 18966, F3, 3, 34) (dual of [(18966, 3), 56675, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3223, 18966, F3, 5, 34) (dual of [(18966, 5), 94607, 35]-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.