Best Known (147−23, 147, s)-Nets in Base 4
(147−23, 147, 5962)-Net over F4 — Constructive and digital
Digital (124, 147, 5962)-net over F4, using
- net defined by OOA [i] based on linear OOA(4147, 5962, F4, 23, 23) (dual of [(5962, 23), 136979, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4147, 65583, F4, 23) (dual of [65583, 65436, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4147, 65586, F4, 23) (dual of [65586, 65439, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(4147, 65586, F4, 23) (dual of [65586, 65439, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4147, 65583, F4, 23) (dual of [65583, 65436, 24]-code), using
(147−23, 147, 44357)-Net over F4 — Digital
Digital (124, 147, 44357)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4147, 44357, F4, 23) (dual of [44357, 44210, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4147, 65586, F4, 23) (dual of [65586, 65439, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(4147, 65586, F4, 23) (dual of [65586, 65439, 24]-code), using
(147−23, 147, large)-Net in Base 4 — Upper bound on s
There is no (124, 147, large)-net in base 4, because
- 21 times m-reduction [i] would yield (124, 126, large)-net in base 4, but