Information on Result #1744010
Digital (18, 34, 684)-net over F64, using net defined by OOA based on linear OOA(6434, 684, F64, 21, 16) (dual of [(684, 21), 14330, 17]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(6434, 2053, F64, 3, 16) (dual of [(2053, 3), 6125, 17]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6434, 2053, F64, 2, 16) (dual of [(2053, 2), 4072, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6434, 4106, F64, 16) (dual of [4106, 4072, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6434, 4107, F64, 16) (dual of [4107, 4073, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(6423, 4096, F64, 12) (dual of [4096, 4073, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(6434, 4107, F64, 16) (dual of [4107, 4073, 17]-code), using
- OOA 2-folding [i] based on linear OA(6434, 4106, F64, 16) (dual of [4106, 4072, 17]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6434, 2053, F64, 2, 16) (dual of [(2053, 2), 4072, 17]-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.