Best Known (78, 96, s)-Nets in Base 3
(78, 96, 729)-Net over F3 — Constructive and digital
Digital (78, 96, 729)-net over F3, using
- net defined by OOA [i] based on linear OOA(396, 729, F3, 18, 18) (dual of [(729, 18), 13026, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(396, 6561, F3, 18) (dual of [6561, 6465, 19]-code), using
- 1 times truncation [i] based on linear OA(397, 6562, F3, 19) (dual of [6562, 6465, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(397, 6562, F3, 19) (dual of [6562, 6465, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(396, 6561, F3, 18) (dual of [6561, 6465, 19]-code), using
(78, 96, 3124)-Net over F3 — Digital
Digital (78, 96, 3124)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(396, 3124, F3, 2, 18) (dual of [(3124, 2), 6152, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(396, 3280, F3, 2, 18) (dual of [(3280, 2), 6464, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(396, 6560, F3, 18) (dual of [6560, 6464, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(396, 6561, F3, 18) (dual of [6561, 6465, 19]-code), using
- 1 times truncation [i] based on linear OA(397, 6562, F3, 19) (dual of [6562, 6465, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(397, 6562, F3, 19) (dual of [6562, 6465, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(396, 6561, F3, 18) (dual of [6561, 6465, 19]-code), using
- OOA 2-folding [i] based on linear OA(396, 6560, F3, 18) (dual of [6560, 6464, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(396, 3280, F3, 2, 18) (dual of [(3280, 2), 6464, 19]-NRT-code), using
(78, 96, 254683)-Net in Base 3 — Upper bound on s
There is no (78, 96, 254684)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6362 859499 543544 325518 963268 523671 640621 477945 > 396 [i]