Best Known (116−9, 116, s)-Nets in Base 4
(116−9, 116, large)-Net over F4 — Constructive and digital
Digital (107, 116, large)-net over F4, using
- trace code for nets [i] based on digital (20, 29, 2097406)-net over F256, using
- net defined by OOA [i] based on linear OOA(25629, 2097406, F256, 12, 9) (dual of [(2097406, 12), 25168843, 10]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(25629, 2097407, F256, 4, 9) (dual of [(2097407, 4), 8389599, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2564, 257, F256, 4, 4) (dual of [(257, 4), 1024, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;1024,256) [i]
- linear OOA(25625, 2097150, F256, 4, 9) (dual of [(2097150, 4), 8388575, 10]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25625, 8388600, F256, 9) (dual of [8388600, 8388575, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- OOA 4-folding [i] based on linear OA(25625, 8388600, F256, 9) (dual of [8388600, 8388575, 10]-code), using
- linear OOA(2564, 257, F256, 4, 4) (dual of [(257, 4), 1024, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(25629, 2097407, F256, 4, 9) (dual of [(2097407, 4), 8389599, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(25629, 2097406, F256, 12, 9) (dual of [(2097406, 12), 25168843, 10]-NRT-code), using
(116−9, 116, large)-Net in Base 4 — Upper bound on s
There is no (107, 116, large)-net in base 4, because
- 7 times m-reduction [i] would yield (107, 109, large)-net in base 4, but