Best Known (169−29, 169, s)-Nets in Base 4
(169−29, 169, 4681)-Net over F4 — Constructive and digital
Digital (140, 169, 4681)-net over F4, using
- net defined by OOA [i] based on linear OOA(4169, 4681, F4, 29, 29) (dual of [(4681, 29), 135580, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4169, 65535, F4, 29) (dual of [65535, 65366, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4169, 65535, F4, 29) (dual of [65535, 65366, 30]-code), using
(169−29, 169, 25876)-Net over F4 — Digital
Digital (140, 169, 25876)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4169, 25876, F4, 2, 29) (dual of [(25876, 2), 51583, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4169, 32768, F4, 2, 29) (dual of [(32768, 2), 65367, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- OOA 2-folding [i] based on linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using
- discarding factors / shortening the dual code based on linear OOA(4169, 32768, F4, 2, 29) (dual of [(32768, 2), 65367, 30]-NRT-code), using
(169−29, 169, large)-Net in Base 4 — Upper bound on s
There is no (140, 169, large)-net in base 4, because
- 27 times m-reduction [i] would yield (140, 142, large)-net in base 4, but