Information on Result #1707838
Digital (53, 59, 4783000)-net over F3, using net defined by OOA based on linear OOA(359, 4783000, F3, 6, 6) (dual of [(4783000, 6), 28697941, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(359, 4783000, F3, 5, 6) (dual of [(4783000, 5), 23914941, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(359, 4783000, F3, 6) (dual of [4783000, 4782941, 7]-code), using
- 1 times code embedding in larger space [i] based on linear OA(358, 4782999, F3, 6) (dual of [4782999, 4782941, 7]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(357, 4782969, F3, 7) (dual of [4782969, 4782912, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(329, 4782969, F3, 4) (dual of [4782969, 4782940, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(329, 30, F3, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
- dual of repetition code with length 30 [i]
- linear OA(31, 30, F3, 1) (dual of [30, 29, 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
- 1 times code embedding in larger space [i] based on linear OA(358, 4782999, F3, 6) (dual of [4782999, 4782941, 7]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(359, 4783000, F3, 6) (dual of [4783000, 4782941, 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.