Best Known (30, 30+6, s)-Nets in Base 3
(30, 30+6, 6561)-Net over F3 — Constructive and digital
Digital (30, 36, 6561)-net over F3, using
- net defined by OOA [i] based on linear OOA(336, 6561, F3, 6, 6) (dual of [(6561, 6), 39330, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(336, 6561, F3, 5, 6) (dual of [(6561, 5), 32769, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(336, 19683, F3, 6) (dual of [19683, 19647, 7]-code), using
- 1 times truncation [i] based on linear OA(337, 19684, F3, 7) (dual of [19684, 19647, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(337, 19684, F3, 7) (dual of [19684, 19647, 8]-code), using
- OA 3-folding and stacking [i] based on linear OA(336, 19683, F3, 6) (dual of [19683, 19647, 7]-code), using
- appending kth column [i] based on linear OOA(336, 6561, F3, 5, 6) (dual of [(6561, 5), 32769, 7]-NRT-code), using
(30, 30+6, 16548)-Net over F3 — Digital
Digital (30, 36, 16548)-net over F3, using
- net defined by OOA [i] based on linear OOA(336, 16548, F3, 6, 6) (dual of [(16548, 6), 99252, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(336, 16548, F3, 5, 6) (dual of [(16548, 5), 82704, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(336, 16548, F3, 6) (dual of [16548, 16512, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(336, 19683, F3, 6) (dual of [19683, 19647, 7]-code), using
- 1 times truncation [i] based on linear OA(337, 19684, F3, 7) (dual of [19684, 19647, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(337, 19684, F3, 7) (dual of [19684, 19647, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(336, 19683, F3, 6) (dual of [19683, 19647, 7]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(336, 16548, F3, 6) (dual of [16548, 16512, 7]-code), using
- appending kth column [i] based on linear OOA(336, 16548, F3, 5, 6) (dual of [(16548, 5), 82704, 7]-NRT-code), using
(30, 30+6, 482843)-Net in Base 3 — Upper bound on s
There is no (30, 36, 482844)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 150094 922066 455185 > 336 [i]