Best Known (39, 48, s)-Nets in Base 4
(39, 48, 4106)-Net over F4 — Constructive and digital
Digital (39, 48, 4106)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 10)-net over F4, using
- digital (34, 43, 4096)-net over F4, using
- net defined by OOA [i] based on linear OOA(443, 4096, F4, 9, 9) (dual of [(4096, 9), 36821, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(443, 16385, F4, 9) (dual of [16385, 16342, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(443, 16385, F4, 9) (dual of [16385, 16342, 10]-code), using
- net defined by OOA [i] based on linear OOA(443, 4096, F4, 9, 9) (dual of [(4096, 9), 36821, 10]-NRT-code), using
(39, 48, 12417)-Net over F4 — Digital
Digital (39, 48, 12417)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(448, 12417, F4, 9) (dual of [12417, 12369, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(448, 16396, F4, 9) (dual of [16396, 16348, 10]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(448, 16396, F4, 9) (dual of [16396, 16348, 10]-code), using
(39, 48, large)-Net in Base 4 — Upper bound on s
There is no (39, 48, large)-net in base 4, because
- 7 times m-reduction [i] would yield (39, 41, large)-net in base 4, but