Best Known (153, 153+28, s)-Nets in Base 3
(153, 153+28, 4217)-Net over F3 — Constructive and digital
Digital (153, 181, 4217)-net over F3, using
- net defined by OOA [i] based on linear OOA(3181, 4217, F3, 28, 28) (dual of [(4217, 28), 117895, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3181, 59038, F3, 28) (dual of [59038, 58857, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3181, 59038, F3, 28) (dual of [59038, 58857, 29]-code), using
(153, 153+28, 16920)-Net over F3 — Digital
Digital (153, 181, 16920)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3181, 16920, F3, 3, 28) (dual of [(16920, 3), 50579, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3181, 19683, F3, 3, 28) (dual of [(19683, 3), 58868, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- OOA 3-folding [i] based on linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(3181, 19683, F3, 3, 28) (dual of [(19683, 3), 58868, 29]-NRT-code), using
(153, 153+28, 4455768)-Net in Base 3 — Upper bound on s
There is no (153, 181, 4455769)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 228 532176 548223 243753 325972 147106 616893 556271 809835 601135 863747 660985 006817 798398 923881 > 3181 [i]