Best Known (113, 113+11, s)-Nets in Base 4
(113, 113+11, 6710880)-Net over F4 — Constructive and digital
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
(113, 113+11, large)-Net over F4 — Digital
Digital (113, 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
(113, 113+11, large)-Net in Base 4 — Upper bound on s
There is no (113, 124, large)-net in base 4, because
- 9 times m-reduction [i] would yield (113, 115, large)-net in base 4, but