Information on Result #598898
There is no digital (130, 260, 273)-net over F2, because extracting embedded orthogonal array would yield linear OA(2260, 273, F2, 130) (dual of [273, 13, 131]-code), but
- construction Y1 [i] would yield
- linear OA(2259, 269, F2, 130) (dual of [269, 10, 131]-code), but
- residual code [i] would yield linear OA(2129, 138, F2, 65) (dual of [138, 9, 66]-code), but
- 1 times truncation [i] would yield linear OA(2128, 137, F2, 64) (dual of [137, 9, 65]-code), but
- residual code [i] would yield linear OA(264, 72, F2, 32) (dual of [72, 8, 33]-code), but
- adding a parity check bit [i] would yield linear OA(265, 73, F2, 33) (dual of [73, 8, 34]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(265, 73, F2, 33) (dual of [73, 8, 34]-code), but
- residual code [i] would yield linear OA(264, 72, F2, 32) (dual of [72, 8, 33]-code), but
- 1 times truncation [i] would yield linear OA(2128, 137, F2, 64) (dual of [137, 9, 65]-code), but
- residual code [i] would yield linear OA(2129, 138, F2, 65) (dual of [138, 9, 66]-code), but
- OA(213, 273, S2, 4), but
- discarding factors would yield OA(213, 128, S2, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 8257 > 213 [i]
- discarding factors would yield OA(213, 128, S2, 4), but
- linear OA(2259, 269, F2, 130) (dual of [269, 10, 131]-code), but
Mode: Bound (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.