Best Known (127, 138, s)-Nets in Base 4
(127, 138, 6711120)-Net over F4 — Constructive and digital
Digital (127, 138, 6711120)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (9, 14, 240)-net over F4, using
- net defined by OOA [i] based on linear OOA(414, 240, F4, 5, 5) (dual of [(240, 5), 1186, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(414, 481, F4, 5) (dual of [481, 467, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 482, F4, 5) (dual of [482, 468, 6]-code), using
- trace code [i] based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 482, F4, 5) (dual of [482, 468, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(414, 481, F4, 5) (dual of [481, 467, 6]-code), using
- net defined by OOA [i] based on linear OOA(414, 240, F4, 5, 5) (dual of [(240, 5), 1186, 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 (9, 14, 240)-net over F4, using
(127, 138, large)-Net over F4 — Digital
Digital (127, 138, large)-net over F4, using
- 43 times duplication [i] based on digital (124, 135, large)-net over F4, using
- t-expansion [i] based on digital (121, 135, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4135, large, F4, 14) (dual of [large, large−135, 15]-code), using
- 14 times code embedding in larger space [i] based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 14 times code embedding in larger space [i] based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4135, large, F4, 14) (dual of [large, large−135, 15]-code), using
- t-expansion [i] based on digital (121, 135, large)-net over F4, using
(127, 138, large)-Net in Base 4 — Upper bound on s
There is no (127, 138, large)-net in base 4, because
- 9 times m-reduction [i] would yield (127, 129, large)-net in base 4, but