Best Known (142, 164, s)-Nets in Base 4
(142, 164, 95327)-Net over F4 — Constructive and digital
Digital (142, 164, 95327)-net over F4, using
- net defined by OOA [i] based on linear OOA(4164, 95327, F4, 22, 22) (dual of [(95327, 22), 2097030, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(4164, 1048597, F4, 22) (dual of [1048597, 1048433, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- OA 11-folding and stacking [i] based on linear OA(4164, 1048597, F4, 22) (dual of [1048597, 1048433, 23]-code), using
(142, 164, 359277)-Net over F4 — Digital
Digital (142, 164, 359277)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4164, 359277, F4, 2, 22) (dual of [(359277, 2), 718390, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4164, 524298, F4, 2, 22) (dual of [(524298, 2), 1048432, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4164, 1048596, F4, 22) (dual of [1048596, 1048432, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4164, 1048597, F4, 22) (dual of [1048597, 1048433, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(4164, 1048597, F4, 22) (dual of [1048597, 1048433, 23]-code), using
- OOA 2-folding [i] based on linear OA(4164, 1048596, F4, 22) (dual of [1048596, 1048432, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(4164, 524298, F4, 2, 22) (dual of [(524298, 2), 1048432, 23]-NRT-code), using
(142, 164, large)-Net in Base 4 — Upper bound on s
There is no (142, 164, large)-net in base 4, because
- 20 times m-reduction [i] would yield (142, 144, large)-net in base 4, but