Best Known (150, 168, s)-Nets in Base 3
(150, 168, 531441)-Net over F3 — Constructive and digital
Digital (150, 168, 531441)-net over F3, using
- net defined by OOA [i] based on linear OOA(3168, 531441, F3, 18, 18) (dual of [(531441, 18), 9565770, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3168, 4782969, F3, 18) (dual of [4782969, 4782801, 19]-code), using
- 1 times truncation [i] based on linear OA(3169, 4782970, F3, 19) (dual of [4782970, 4782801, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, 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(3169, 4782970, F3, 19) (dual of [4782970, 4782801, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(3168, 4782969, F3, 18) (dual of [4782969, 4782801, 19]-code), using
(150, 168, 1269516)-Net over F3 — Digital
Digital (150, 168, 1269516)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3168, 1269516, F3, 3, 18) (dual of [(1269516, 3), 3808380, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3168, 1594323, F3, 3, 18) (dual of [(1594323, 3), 4782801, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3168, 4782969, F3, 18) (dual of [4782969, 4782801, 19]-code), using
- 1 times truncation [i] based on linear OA(3169, 4782970, F3, 19) (dual of [4782970, 4782801, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, 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(3169, 4782970, F3, 19) (dual of [4782970, 4782801, 20]-code), using
- OOA 3-folding [i] based on linear OA(3168, 4782969, F3, 18) (dual of [4782969, 4782801, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(3168, 1594323, F3, 3, 18) (dual of [(1594323, 3), 4782801, 19]-NRT-code), using
(150, 168, large)-Net in Base 3 — Upper bound on s
There is no (150, 168, large)-net in base 3, because
- 16 times m-reduction [i] would yield (150, 152, large)-net in base 3, but