Information on Result #1713690
Digital (156, 172, 2097177)-net over F3, using net defined by OOA based on linear OOA(3172, 2097177, F3, 20, 16) (dual of [(2097177, 20), 41943368, 17]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3172, 4194355, F3, 4, 16) (dual of [(4194355, 4), 16777248, 17]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3172, 4194355, F3, 2, 16) (dual of [(4194355, 2), 8388538, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(321, 54, F3, 2, 8) (dual of [(54, 2), 87, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(321, 54, F3, 8) (dual of [54, 33, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(321, 54, F3, 8) (dual of [54, 33, 9]-code), using
- linear OOA(3151, 4194301, F3, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- OOA 2-folding [i] based on linear OA(3151, 8388602, F3, 16) (dual of [8388602, 8388451, 17]-code), using
- linear OOA(321, 54, F3, 2, 8) (dual of [(54, 2), 87, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3172, 4194355, F3, 2, 16) (dual of [(4194355, 2), 8388538, 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.