Best Known (122−10, 122, s)-Nets in Base 4
(122−10, 122, 6710944)-Net over F4 — Constructive and digital
Digital (112, 122, 6710944)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 10, 64)-net over F4, using
- digital (102, 112, 6710880)-net over F4, using
- trace code for nets [i] based on digital (18, 28, 1677720)-net over F256, using
- net defined by OOA [i] based on linear OOA(25628, 1677720, F256, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(25628, 8388600, F256, 10) (dual of [8388600, 8388572, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(25628, 8388600, F256, 10) (dual of [8388600, 8388572, 11]-code), using
- net defined by OOA [i] based on linear OOA(25628, 1677720, F256, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
- trace code for nets [i] based on digital (18, 28, 1677720)-net over F256, using
(122−10, 122, large)-Net over F4 — Digital
Digital (112, 122, large)-net over F4, using
- t-expansion [i] based on digital (111, 122, large)-net over F4, using
- 2 times m-reduction [i] based on digital (111, 124, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4124, large, F4, 13) (dual of [large, large−124, 14]-code), using
- 15 times code embedding in larger space [i] based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 15 times code embedding in larger space [i] based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4124, large, F4, 13) (dual of [large, large−124, 14]-code), using
- 2 times m-reduction [i] based on digital (111, 124, large)-net over F4, using
(122−10, 122, large)-Net in Base 4 — Upper bound on s
There is no (112, 122, large)-net in base 4, because
- 8 times m-reduction [i] would yield (112, 114, large)-net in base 4, but