Best Known (144−18, 144, s)-Nets in Base 3
(144−18, 144, 59049)-Net over F3 — Constructive and digital
Digital (126, 144, 59049)-net over F3, using
- net defined by OOA [i] based on linear OOA(3144, 59049, F3, 18, 18) (dual of [(59049, 18), 1062738, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3144, 531441, F3, 18) (dual of [531441, 531297, 19]-code), using
- 1 times truncation [i] based on linear OA(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, 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(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(3144, 531441, F3, 18) (dual of [531441, 531297, 19]-code), using
(144−18, 144, 177147)-Net over F3 — Digital
Digital (126, 144, 177147)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3144, 177147, F3, 3, 18) (dual of [(177147, 3), 531297, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3144, 531441, F3, 18) (dual of [531441, 531297, 19]-code), using
- 1 times truncation [i] based on linear OA(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, 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(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using
- OOA 3-folding [i] based on linear OA(3144, 531441, F3, 18) (dual of [531441, 531297, 19]-code), using
(144−18, 144, large)-Net in Base 3 — Upper bound on s
There is no (126, 144, large)-net in base 3, because
- 16 times m-reduction [i] would yield (126, 128, large)-net in base 3, but