Best Known (120, 120+10, s)-Nets in Base 4
(120, 120+10, 6711396)-Net over F4 — Constructive and digital
Digital (120, 130, 6711396)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (13, 18, 516)-net over F4, using
- net defined by OOA [i] based on linear OOA(418, 516, F4, 6, 5) (dual of [(516, 6), 3078, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(418, 517, F4, 2, 5) (dual of [(517, 2), 1016, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(42, 5, F4, 2, 2) (dual of [(5, 2), 8, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;8,4) [i]
- linear OOA(416, 512, F4, 2, 5) (dual of [(512, 2), 1008, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(416, 1024, F4, 5) (dual of [1024, 1008, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- OOA 2-folding [i] based on linear OA(416, 1024, F4, 5) (dual of [1024, 1008, 6]-code), using
- linear OOA(42, 5, F4, 2, 2) (dual of [(5, 2), 8, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(418, 517, F4, 2, 5) (dual of [(517, 2), 1016, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(418, 516, F4, 6, 5) (dual of [(516, 6), 3078, 6]-NRT-code), 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
- digital (13, 18, 516)-net over F4, using
(120, 120+10, 6711872)-Net in Base 4 — Constructive
(120, 130, 6711872)-net in base 4, using
- (u, u+v)-construction [i] based on
- (13, 18, 992)-net in base 4, using
- net defined by OOA [i] based on OOA(418, 992, S4, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(418, 1985, S4, 5), using
- discarding factors based on OA(418, 1986, S4, 5), using
- trace code [i] based on OA(169, 993, S16, 5), using
- discarding parts of the base [i] based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- trace code [i] based on OA(169, 993, S16, 5), using
- discarding factors based on OA(418, 1986, S4, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(418, 1985, S4, 5), using
- net defined by OOA [i] based on OOA(418, 992, S4, 5, 5), 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
- (13, 18, 992)-net in base 4, using
(120, 120+10, large)-Net over F4 — Digital
Digital (120, 130, large)-net over F4, using
- 46 times duplication [i] based on digital (114, 124, large)-net over F4, using
- t-expansion [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
- t-expansion [i] based on digital (111, 124, large)-net over F4, using
(120, 120+10, large)-Net in Base 4 — Upper bound on s
There is no (120, 130, large)-net in base 4, because
- 8 times m-reduction [i] would yield (120, 122, large)-net in base 4, but