Best Known (171, 171+32, s)-Nets in Base 4
(171, 171+32, 4099)-Net over F4 — Constructive and digital
Digital (171, 203, 4099)-net over F4, using
- net defined by OOA [i] based on linear OOA(4203, 4099, F4, 32, 32) (dual of [(4099, 32), 130965, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(4203, 65584, F4, 32) (dual of [65584, 65381, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(4203, 65586, F4, 32) (dual of [65586, 65383, 33]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(410, 50, F4, 5) (dual of [50, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(4203, 65586, F4, 32) (dual of [65586, 65383, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(4203, 65584, F4, 32) (dual of [65584, 65381, 33]-code), using
(171, 171+32, 45426)-Net over F4 — Digital
Digital (171, 203, 45426)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4203, 45426, F4, 32) (dual of [45426, 45223, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(4203, 65586, F4, 32) (dual of [65586, 65383, 33]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(410, 50, F4, 5) (dual of [50, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(4203, 65586, F4, 32) (dual of [65586, 65383, 33]-code), using
(171, 171+32, large)-Net in Base 4 — Upper bound on s
There is no (171, 203, large)-net in base 4, because
- 30 times m-reduction [i] would yield (171, 173, large)-net in base 4, but