Best Known (112−22, 112, s)-Nets in Base 5
(112−22, 112, 1424)-Net over F5 — Constructive and digital
Digital (90, 112, 1424)-net over F5, using
- net defined by OOA [i] based on linear OOA(5112, 1424, F5, 22, 22) (dual of [(1424, 22), 31216, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(5112, 15664, F5, 22) (dual of [15664, 15552, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(5103, 15625, F5, 22) (dual of [15625, 15522, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(59, 39, F5, 5) (dual of [39, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- OA 11-folding and stacking [i] based on linear OA(5112, 15664, F5, 22) (dual of [15664, 15552, 23]-code), using
(112−22, 112, 15664)-Net over F5 — Digital
Digital (90, 112, 15664)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5112, 15664, F5, 22) (dual of [15664, 15552, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(5103, 15625, F5, 22) (dual of [15625, 15522, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(59, 39, F5, 5) (dual of [39, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
(112−22, 112, large)-Net in Base 5 — Upper bound on s
There is no (90, 112, large)-net in base 5, because
- 20 times m-reduction [i] would yield (90, 92, large)-net in base 5, but