Best Known (185, 209, s)-Nets in Base 4
(185, 209, 349530)-Net over F4 — Constructive and digital
Digital (185, 209, 349530)-net over F4, using
- net defined by OOA [i] based on linear OOA(4209, 349530, F4, 24, 24) (dual of [(349530, 24), 8388511, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4209, 4194360, F4, 24) (dual of [4194360, 4194151, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4209, 4194368, F4, 24) (dual of [4194368, 4194159, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(4199, 4194304, F4, 25) (dual of [4194304, 4194105, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4144, 4194304, F4, 18) (dual of [4194304, 4194160, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(4209, 4194368, F4, 24) (dual of [4194368, 4194159, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(4209, 4194360, F4, 24) (dual of [4194360, 4194151, 25]-code), using
(185, 209, 2097184)-Net over F4 — Digital
Digital (185, 209, 2097184)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4209, 2097184, F4, 2, 24) (dual of [(2097184, 2), 4194159, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4209, 4194368, F4, 24) (dual of [4194368, 4194159, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(4199, 4194304, F4, 25) (dual of [4194304, 4194105, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4144, 4194304, F4, 18) (dual of [4194304, 4194160, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- OOA 2-folding [i] based on linear OA(4209, 4194368, F4, 24) (dual of [4194368, 4194159, 25]-code), using
(185, 209, large)-Net in Base 4 — Upper bound on s
There is no (185, 209, large)-net in base 4, because
- 22 times m-reduction [i] would yield (185, 187, large)-net in base 4, but