Best Known (140, 168, s)-Nets in Base 4
(140, 168, 4681)-Net over F4 — Constructive and digital
Digital (140, 168, 4681)-net over F4, using
- net defined by OOA [i] based on linear OOA(4168, 4681, F4, 28, 28) (dual of [(4681, 28), 130900, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(4168, 65534, F4, 28) (dual of [65534, 65366, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4168, 65535, F4, 28) (dual of [65535, 65367, 29]-code), using
- 1 times truncation [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]
- 1 times truncation [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 OA(4168, 65535, F4, 28) (dual of [65535, 65367, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(4168, 65534, F4, 28) (dual of [65534, 65366, 29]-code), using
(140, 168, 32767)-Net over F4 — Digital
Digital (140, 168, 32767)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4168, 32767, F4, 2, 28) (dual of [(32767, 2), 65366, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4168, 65534, F4, 28) (dual of [65534, 65366, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4168, 65535, F4, 28) (dual of [65535, 65367, 29]-code), using
- 1 times truncation [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]
- 1 times truncation [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 OA(4168, 65535, F4, 28) (dual of [65535, 65367, 29]-code), using
- OOA 2-folding [i] based on linear OA(4168, 65534, F4, 28) (dual of [65534, 65366, 29]-code), using
(140, 168, large)-Net in Base 4 — Upper bound on s
There is no (140, 168, large)-net in base 4, because
- 26 times m-reduction [i] would yield (140, 142, large)-net in base 4, but