Information on Result #1728808
Digital (133, 157, 524301)-net over F8, using net defined by OOA based on linear OOA(8157, 524301, F8, 27, 24) (dual of [(524301, 27), 14155970, 25]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(8157, 2097205, F8, 3, 24) (dual of [(2097205, 3), 6291458, 25]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8157, 2097205, F8, 24) (dual of [2097205, 2097048, 25]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8155, 2097201, F8, 24) (dual of [2097201, 2097046, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(87, 49, F8, 5) (dual of [49, 42, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(8155, 2097203, F8, 23) (dual of [2097203, 2097048, 24]-code), using Gilbert–Varšamov bound and bm = 8155 > Vbs−1(k−1) = 41440 872736 745127 272002 774503 496160 501227 956327 177782 565907 077514 283975 281604 543243 517213 130336 527517 439568 024077 374150 980318 972194 693584 [i]
- linear OA(80, 2, F8, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(8155, 2097201, F8, 24) (dual of [2097201, 2097046, 25]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8157, 2097205, F8, 24) (dual of [2097205, 2097048, 25]-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.