Best Known (84−16, 84, s)-Nets in Base 8
(84−16, 84, 32768)-Net over F8 — Constructive and digital
Digital (68, 84, 32768)-net over F8, using
- net defined by OOA [i] based on linear OOA(884, 32768, F8, 16, 16) (dual of [(32768, 16), 524204, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(884, 262144, F8, 16) (dual of [262144, 262060, 17]-code), using
- 1 times truncation [i] based on linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, 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(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(884, 262144, F8, 16) (dual of [262144, 262060, 17]-code), using
(84−16, 84, 195153)-Net over F8 — Digital
Digital (68, 84, 195153)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(884, 195153, F8, 16) (dual of [195153, 195069, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(884, 262144, F8, 16) (dual of [262144, 262060, 17]-code), using
- 1 times truncation [i] based on linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, 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(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(884, 262144, F8, 16) (dual of [262144, 262060, 17]-code), using
(84−16, 84, large)-Net in Base 8 — Upper bound on s
There is no (68, 84, large)-net in base 8, because
- 14 times m-reduction [i] would yield (68, 70, large)-net in base 8, but