Best Known (52, 60, s)-Nets in Base 4
(52, 60, 262144)-Net over F4 — Constructive and digital
Digital (52, 60, 262144)-net over F4, using
- net defined by OOA [i] based on linear OOA(460, 262144, F4, 8, 8) (dual of [(262144, 8), 2097092, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(460, 1048576, F4, 8) (dual of [1048576, 1048516, 9]-code), using
- 1 times truncation [i] based on linear OA(461, 1048577, F4, 9) (dual of [1048577, 1048516, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(461, 1048577, F4, 9) (dual of [1048577, 1048516, 10]-code), using
- OA 4-folding and stacking [i] based on linear OA(460, 1048576, F4, 8) (dual of [1048576, 1048516, 9]-code), using
(52, 60, 830530)-Net over F4 — Digital
Digital (52, 60, 830530)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(460, 830530, F4, 8) (dual of [830530, 830470, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(460, 1048576, F4, 8) (dual of [1048576, 1048516, 9]-code), using
- 1 times truncation [i] based on linear OA(461, 1048577, F4, 9) (dual of [1048577, 1048516, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(461, 1048577, F4, 9) (dual of [1048577, 1048516, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(460, 1048576, F4, 8) (dual of [1048576, 1048516, 9]-code), using
(52, 60, large)-Net in Base 4 — Upper bound on s
There is no (52, 60, large)-net in base 4, because
- 6 times m-reduction [i] would yield (52, 54, large)-net in base 4, but