Best Known (156−9, 156, s)-Nets in Base 4
(156−9, 156, large)-Net over F4 — Constructive and digital
Digital (147, 156, large)-net over F4, using
- 2 times m-reduction [i] based on digital (147, 158, large)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (29, 34, 2097151)-net over F4, using
- net defined by OOA [i] based on linear OOA(434, 2097151, F4, 5, 5) (dual of [(2097151, 5), 10485721, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(434, 4194303, F4, 5) (dual of [4194303, 4194269, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(434, 4194304, F4, 5) (dual of [4194304, 4194270, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(434, 4194304, F4, 5) (dual of [4194304, 4194270, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(434, 4194303, F4, 5) (dual of [4194303, 4194269, 6]-code), using
- net defined by OOA [i] based on linear OOA(434, 2097151, F4, 5, 5) (dual of [(2097151, 5), 10485721, 6]-NRT-code), using
- digital (113, 124, 6710880)-net over F4, using
- trace code for nets [i] based on digital (20, 31, 1677720)-net over F256, using
- net defined by OOA [i] based on linear OOA(25631, 1677720, F256, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25631, 8388601, F256, 11) (dual of [8388601, 8388570, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25631, 8388601, F256, 11) (dual of [8388601, 8388570, 12]-code), using
- net defined by OOA [i] based on linear OOA(25631, 1677720, F256, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
- trace code for nets [i] based on digital (20, 31, 1677720)-net over F256, using
- digital (29, 34, 2097151)-net over F4, using
- (u, u+v)-construction [i] based on
(156−9, 156, large)-Net in Base 4 — Upper bound on s
There is no (147, 156, large)-net in base 4, because
- 7 times m-reduction [i] would yield (147, 149, large)-net in base 4, but