Best Known (36, 36+10, s)-Nets in Base 64
(36, 36+10, 1679801)-Net over F64 — Constructive and digital
Digital (36, 46, 1679801)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (4, 9, 2081)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 65)-net over F64, using
- digital (2, 7, 2016)-net over F64, using
- net defined by OOA [i] based on linear OOA(647, 2016, F64, 5, 5) (dual of [(2016, 5), 10073, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- net defined by OOA [i] based on linear OOA(647, 2016, F64, 5, 5) (dual of [(2016, 5), 10073, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- digital (27, 37, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- digital (4, 9, 2081)-net over F64, using
(36, 36+10, 1685848)-Net in Base 64 — Constructive
(36, 46, 1685848)-net in base 64, using
- (u, u+v)-construction [i] based on
- (4, 9, 8128)-net in base 64, using
- net defined by OOA [i] based on OOA(649, 8128, S64, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(649, 16257, S64, 5), using
- discarding parts of the base [i] based on linear OA(1287, 16257, F128, 5) (dual of [16257, 16250, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(649, 16257, S64, 5), using
- net defined by OOA [i] based on OOA(649, 8128, S64, 5, 5), using
- digital (27, 37, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- (4, 9, 8128)-net in base 64, using
(36, 36+10, large)-Net over F64 — Digital
Digital (36, 46, large)-net over F64, using
- t-expansion [i] based on digital (34, 46, large)-net over F64, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6446, large, F64, 12) (dual of [large, large−46, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 1 times code embedding in larger space [i] based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6446, large, F64, 12) (dual of [large, large−46, 13]-code), using
(36, 36+10, large)-Net in Base 64 — Upper bound on s
There is no (36, 46, large)-net in base 64, because
- 8 times m-reduction [i] would yield (36, 38, large)-net in base 64, but