Information on Result #1210782
Digital (132, 151, 116518)-net over F4, using (u, u+v)-construction based on
- digital (1, 10, 9)-net over F4, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- digital (122, 141, 116509)-net over F4, using
- net defined by OOA [i] based on linear OOA(4141, 116509, F4, 19, 19) (dual of [(116509, 19), 2213530, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4141, 1048582, F4, 19) (dual of [1048582, 1048441, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4141, 1048586, F4, 19) (dual of [1048586, 1048445, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(4141, 1048576, F4, 19) (dual of [1048576, 1048435, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(4131, 1048576, F4, 18) (dual of [1048576, 1048445, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(40, 10, F4, 0) (dual of [10, 10, 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
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(4141, 1048586, F4, 19) (dual of [1048586, 1048445, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4141, 1048582, F4, 19) (dual of [1048582, 1048441, 20]-code), using
- net defined by OOA [i] based on linear OOA(4141, 116509, F4, 19, 19) (dual of [(116509, 19), 2213530, 20]-NRT-code), using
Mode: Constructive and 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.