Best Known (14, 32, s)-Nets in Base 16
(14, 32, 71)-Net over F16 — Constructive and digital
Digital (14, 32, 71)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- digital (3, 21, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- digital (2, 11, 33)-net over F16, using
(14, 32, 102)-Net over F16 — Digital
Digital (14, 32, 102)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(1632, 102, F16, 2, 18) (dual of [(102, 2), 172, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1632, 128, F16, 2, 18) (dual of [(128, 2), 224, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1632, 256, F16, 18) (dual of [256, 224, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- OOA 2-folding [i] based on linear OA(1632, 256, F16, 18) (dual of [256, 224, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(1632, 128, F16, 2, 18) (dual of [(128, 2), 224, 19]-NRT-code), using
(14, 32, 104)-Net in Base 16 — Constructive
(14, 32, 104)-net in base 16, using
- 1 times m-reduction [i] based on (14, 33, 104)-net in base 16, using
- base change [i] based on digital (3, 22, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- base change [i] based on digital (3, 22, 104)-net over F64, using
(14, 32, 113)-Net in Base 16
(14, 32, 113)-net in base 16, using
- 1 times m-reduction [i] based on (14, 33, 113)-net in base 16, using
- base change [i] based on digital (3, 22, 113)-net over F64, using
- net from sequence [i] based on digital (3, 112)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
- net from sequence [i] based on digital (3, 112)-sequence over F64, using
- base change [i] based on digital (3, 22, 113)-net over F64, using
(14, 32, 5279)-Net in Base 16 — Upper bound on s
There is no (14, 32, 5280)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 340 538765 906858 567671 995663 342014 439301 > 1632 [i]