Best Known (64, 64+11, s)-Nets in Base 16
(64, 64+11, 3388080)-Net over F16 — Constructive and digital
Digital (64, 75, 3388080)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (8, 13, 32640)-net over F16, using
- net defined by OOA [i] based on linear OOA(1613, 32640, F16, 5, 5) (dual of [(32640, 5), 163187, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(1613, 65281, F16, 5) (dual of [65281, 65268, 6]-code), using
- net defined by OOA [i] based on linear OOA(1613, 32640, F16, 5, 5) (dual of [(32640, 5), 163187, 6]-NRT-code), using
- digital (51, 62, 3355440)-net over F16, 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 (8, 13, 32640)-net over F16, using
(64, 64+11, large)-Net over F16 — Digital
Digital (64, 75, large)-net over F16, using
- 162 times duplication [i] based on digital (62, 73, large)-net over F16, using
- t-expansion [i] based on digital (60, 73, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1673, large, F16, 13) (dual of [large, large−73, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 1612−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1673, large, F16, 13) (dual of [large, large−73, 14]-code), using
- t-expansion [i] based on digital (60, 73, large)-net over F16, using
(64, 64+11, large)-Net in Base 16 — Upper bound on s
There is no (64, 75, large)-net in base 16, because
- 9 times m-reduction [i] would yield (64, 66, large)-net in base 16, but