Best Known (96−16, 96, s)-Nets in Base 4
(96−16, 96, 8192)-Net over F4 — Constructive and digital
Digital (80, 96, 8192)-net over F4, using
- net defined by OOA [i] based on linear OOA(496, 8192, F4, 16, 16) (dual of [(8192, 16), 130976, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(496, 65536, F4, 16) (dual of [65536, 65440, 17]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(496, 65536, F4, 16) (dual of [65536, 65440, 17]-code), using
(96−16, 96, 32768)-Net over F4 — Digital
Digital (80, 96, 32768)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(496, 32768, F4, 2, 16) (dual of [(32768, 2), 65440, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(496, 65536, F4, 16) (dual of [65536, 65440, 17]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using
- OOA 2-folding [i] based on linear OA(496, 65536, F4, 16) (dual of [65536, 65440, 17]-code), using
(96−16, 96, large)-Net in Base 4 — Upper bound on s
There is no (80, 96, large)-net in base 4, because
- 14 times m-reduction [i] would yield (80, 82, large)-net in base 4, but