Best Known (80, 80+17, s)-Nets in Base 4
(80, 80+17, 8192)-Net over F4 — Constructive and digital
Digital (80, 97, 8192)-net over F4, using
- net defined by OOA [i] based on linear OOA(497, 8192, F4, 17, 17) (dual of [(8192, 17), 139167, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using
(80, 80+17, 24522)-Net over F4 — Digital
Digital (80, 97, 24522)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(497, 24522, F4, 2, 17) (dual of [(24522, 2), 48947, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(497, 32768, F4, 2, 17) (dual of [(32768, 2), 65439, 18]-NRT-code), using
- OOA 2-folding [i] based on 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]
- OOA 2-folding [i] based on linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(497, 32768, F4, 2, 17) (dual of [(32768, 2), 65439, 18]-NRT-code), using
(80, 80+17, large)-Net in Base 4 — Upper bound on s
There is no (80, 97, large)-net in base 4, because
- 15 times m-reduction [i] would yield (80, 82, large)-net in base 4, but