Information on Result #1717384
Digital (61, 69, 2097164)-net over F4, using net defined by OOA based on linear OOA(469, 2097164, F4, 10, 8) (dual of [(2097164, 10), 20971571, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(469, 4194329, F4, 2, 8) (dual of [(4194329, 2), 8388589, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(469, 4194330, F4, 2, 8) (dual of [(4194330, 2), 8388591, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(469, 4194330, F4, 8) (dual of [4194330, 4194261, 9]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(468, 4194328, F4, 8) (dual of [4194328, 4194260, 9]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(467, 4194304, F4, 9) (dual of [4194304, 4194237, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(445, 4194304, F4, 6) (dual of [4194304, 4194259, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
- dual of repetition code with length 24 [i]
- linear OA(41, 24, F4, 1) (dual of [24, 23, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(468, 4194329, F4, 7) (dual of [4194329, 4194261, 8]-code), using Gilbert–Varšamov bound and bm = 468 > Vbs−1(k−1) = 5512 746519 677817 912237 124646 478493 830739 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(468, 4194328, F4, 8) (dual of [4194328, 4194260, 9]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(469, 4194330, F4, 8) (dual of [4194330, 4194261, 9]-code), using
- discarding factors / shortening the dual code based on linear OOA(469, 4194330, F4, 2, 8) (dual of [(4194330, 2), 8388591, 9]-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.