Information on Result #1707822
Digital (45, 51, 531469)-net over F3, using net defined by OOA based on linear OOA(351, 531469, F3, 6, 6) (dual of [(531469, 6), 3188763, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(351, 531469, F3, 5, 6) (dual of [(531469, 5), 2657294, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(351, 531469, F3, 6) (dual of [531469, 531418, 7]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(350, 531467, F3, 6) (dual of [531467, 531417, 7]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(349, 531441, F3, 7) (dual of [531441, 531392, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(325, 531441, F3, 4) (dual of [531441, 531416, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(325, 26, F3, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,3)), using
- dual of repetition code with length 26 [i]
- linear OA(31, 26, F3, 1) (dual of [26, 25, 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(3) [i] based on
- linear OA(350, 531468, F3, 5) (dual of [531468, 531418, 6]-code), using Gilbert–Varšamov bound and bm = 350 > Vbs−1(k−1) = 53187 635733 407401 626299 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 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
- linear OA(350, 531467, F3, 6) (dual of [531467, 531417, 7]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(351, 531469, F3, 6) (dual of [531469, 531418, 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.