Information on Result #1222847
Digital (45, 70, 251)-net over F27, using (u, u+v)-construction based on
- digital (13, 25, 123)-net over F27, using
- net defined by OOA [i] based on linear OOA(2725, 123, F27, 12, 12) (dual of [(123, 12), 1451, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2725, 738, F27, 12) (dual of [738, 713, 13]-code), using
- construction XX applied to C1 = C([725,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([725,8]) [i] based on
- linear OA(2721, 728, F27, 11) (dual of [728, 707, 12]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,7}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2717, 728, F27, 9) (dual of [728, 711, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2723, 728, F27, 12) (dual of [728, 705, 13]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,8}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2715, 728, F27, 8) (dual of [728, 713, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(272, 8, F27, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([725,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([725,8]) [i] based on
- OA 6-folding and stacking [i] based on linear OA(2725, 738, F27, 12) (dual of [738, 713, 13]-code), using
- net defined by OOA [i] based on linear OOA(2725, 123, F27, 12, 12) (dual of [(123, 12), 1451, 13]-NRT-code), using
- digital (20, 45, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 16, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 29, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 16, 64)-net over F27, using
- (u, u+v)-construction [i] based on
Mode: Constructive and 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.