Information on Result #1740772
Digital (18, 30, 675)-net over F32, using net defined by OOA based on linear OOA(3230, 675, F32, 14, 12) (dual of [(675, 14), 9420, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3230, 2026, F32, 2, 12) (dual of [(2026, 2), 4022, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3230, 2026, F32, 12) (dual of [2026, 1996, 13]-code), using
- 992 step Varšamov–Edel lengthening with (ri) = (3, 5 times 0, 1, 31 times 0, 1, 125 times 0, 1, 307 times 0, 1, 519 times 0) [i] based on linear OA(3223, 1027, F32, 12) (dual of [1027, 1004, 13]-code), using
- construction XX applied to C1 = C([1022,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([1022,10]) [i] based on
- linear OA(3221, 1023, F32, 11) (dual of [1023, 1002, 12]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3221, 1023, F32, 11) (dual of [1023, 1002, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3223, 1023, F32, 12) (dual of [1023, 1000, 13]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(3219, 1023, F32, 10) (dual of [1023, 1004, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([1022,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([1022,10]) [i] based on
- 992 step Varšamov–Edel lengthening with (ri) = (3, 5 times 0, 1, 31 times 0, 1, 125 times 0, 1, 307 times 0, 1, 519 times 0) [i] based on linear OA(3223, 1027, F32, 12) (dual of [1027, 1004, 13]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3230, 2026, F32, 12) (dual of [2026, 1996, 13]-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.