Best Known (102, 102+18, s)-Nets in Base 16
(102, 102+18, 1864199)-Net over F16 — Constructive and digital
Digital (102, 120, 1864199)-net over F16, using
- 161 times duplication [i] based on digital (101, 119, 1864199)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 15, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- digital (86, 104, 1864134)-net over F16, using
- trace code for nets [i] based on digital (34, 52, 932067)-net over F256, using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- trace code for nets [i] based on digital (34, 52, 932067)-net over F256, using
- digital (6, 15, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(102, 102+18, 1864214)-Net in Base 16 — Constructive
(102, 120, 1864214)-net in base 16, using
- 161 times duplication [i] based on (101, 119, 1864214)-net in base 16, using
- (u, u+v)-construction [i] based on
- (6, 15, 80)-net in base 16, using
- base change [i] based on digital (1, 10, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- base change [i] based on digital (1, 10, 80)-net over F64, using
- digital (86, 104, 1864134)-net over F16, using
- trace code for nets [i] based on digital (34, 52, 932067)-net over F256, using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- trace code for nets [i] based on digital (34, 52, 932067)-net over F256, using
- (6, 15, 80)-net in base 16, using
- (u, u+v)-construction [i] based on
(102, 102+18, large)-Net over F16 — Digital
Digital (102, 120, large)-net over F16, using
- t-expansion [i] based on digital (99, 120, large)-net over F16, using
- 1 times m-reduction [i] based on digital (99, 121, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16121, large, F16, 22) (dual of [large, large−121, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16121, large, F16, 22) (dual of [large, large−121, 23]-code), using
- 1 times m-reduction [i] based on digital (99, 121, large)-net over F16, using
(102, 102+18, large)-Net in Base 16 — Upper bound on s
There is no (102, 120, large)-net in base 16, because
- 16 times m-reduction [i] would yield (102, 104, large)-net in base 16, but