Best Known (21, 28, s)-Nets in Base 3
(21, 28, 364)-Net over F3 — Constructive and digital
Digital (21, 28, 364)-net over F3, using
- net defined by OOA [i] based on linear OOA(328, 364, F3, 7, 7) (dual of [(364, 7), 2520, 8]-NRT-code), using
(21, 28, 546)-Net over F3 — Digital
Digital (21, 28, 546)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(328, 546, F3, 2, 7) (dual of [(546, 2), 1064, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(328, 1092, F3, 7) (dual of [1092, 1064, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(328, 1093, F3, 7) (dual of [1093, 1065, 8]-code), using
- OOA 2-folding [i] based on linear OA(328, 1092, F3, 7) (dual of [1092, 1064, 8]-code), using
(21, 28, 17880)-Net in Base 3 — Upper bound on s
There is no (21, 28, 17881)-net in base 3, because
- 1 times m-reduction [i] would yield (21, 27, 17881)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 7 625990 908987 > 327 [i]