Best Known (65, 84, s)-Nets in Base 16
(65, 84, 14587)-Net over F16 — Constructive and digital
Digital (65, 84, 14587)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- digital (55, 74, 14563)-net over F16, using
- net defined by OOA [i] based on linear OOA(1674, 14563, F16, 19, 19) (dual of [(14563, 19), 276623, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(1674, 131068, F16, 19) (dual of [131068, 130994, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(1674, 131074, F16, 19) (dual of [131074, 131000, 20]-code), using
- trace code [i] based on linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- trace code [i] based on linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(1674, 131074, F16, 19) (dual of [131074, 131000, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(1674, 131068, F16, 19) (dual of [131068, 130994, 20]-code), using
- net defined by OOA [i] based on linear OOA(1674, 14563, F16, 19, 19) (dual of [(14563, 19), 276623, 20]-NRT-code), using
- digital (1, 10, 24)-net over F16, using
(65, 84, 29127)-Net in Base 16 — Constructive
(65, 84, 29127)-net in base 16, using
- base change [i] based on digital (37, 56, 29127)-net over F64, using
- 641 times duplication [i] based on digital (36, 55, 29127)-net over F64, using
- net defined by OOA [i] based on linear OOA(6455, 29127, F64, 19, 19) (dual of [(29127, 19), 553358, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using
- net defined by OOA [i] based on linear OOA(6455, 29127, F64, 19, 19) (dual of [(29127, 19), 553358, 20]-NRT-code), using
- 641 times duplication [i] based on digital (36, 55, 29127)-net over F64, using
(65, 84, 209548)-Net over F16 — Digital
Digital (65, 84, 209548)-net over F16, using
(65, 84, large)-Net in Base 16 — Upper bound on s
There is no (65, 84, large)-net in base 16, because
- 17 times m-reduction [i] would yield (65, 67, large)-net in base 16, but