Best Known (122, 122+13, s)-Nets in Base 3
(122, 122+13, 1398142)-Net over F3 — Constructive and digital
Digital (122, 135, 1398142)-net over F3, using
- 31 times duplication [i] based on digital (121, 134, 1398142)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (7, 13, 42)-net over F3, using
- digital (108, 121, 1398100)-net over F3, using
- net defined by OOA [i] based on linear OOA(3121, 1398100, F3, 13, 13) (dual of [(1398100, 13), 18175179, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3121, 8388601, F3, 13) (dual of [8388601, 8388480, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3121, 8388601, F3, 13) (dual of [8388601, 8388480, 14]-code), using
- net defined by OOA [i] based on linear OOA(3121, 1398100, F3, 13, 13) (dual of [(1398100, 13), 18175179, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
(122, 122+13, 4194343)-Net over F3 — Digital
Digital (122, 135, 4194343)-net over F3, using
- 31 times duplication [i] based on digital (121, 134, 4194343)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3134, 4194343, F3, 2, 13) (dual of [(4194343, 2), 8388552, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(313, 42, F3, 2, 6) (dual of [(42, 2), 71, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 13, 42)-net over F3, using
- linear OOA(3121, 4194301, F3, 2, 13) (dual of [(4194301, 2), 8388481, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3121, 8388602, F3, 13) (dual of [8388602, 8388481, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
- OOA 2-folding [i] based on linear OA(3121, 8388602, F3, 13) (dual of [8388602, 8388481, 14]-code), using
- linear OOA(313, 42, F3, 2, 6) (dual of [(42, 2), 71, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3134, 4194343, F3, 2, 13) (dual of [(4194343, 2), 8388552, 14]-NRT-code), using
(122, 122+13, large)-Net in Base 3 — Upper bound on s
There is no (122, 135, large)-net in base 3, because
- 11 times m-reduction [i] would yield (122, 124, large)-net in base 3, but