Best Known (147, 147+18, s)-Nets in Base 8
(147, 147+18, 1864394)-Net over F8 — Constructive and digital
Digital (147, 165, 1864394)-net over F8, using
- 81 times duplication [i] based on digital (146, 164, 1864394)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (17, 26, 260)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (4, 8, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 4, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 4, 65)-net over F64, using
- digital (9, 18, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 9, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- trace code for nets [i] based on digital (0, 9, 65)-net over F64, using
- digital (4, 8, 130)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (120, 138, 1864134)-net over F8, using
- trace code for nets [i] based on digital (51, 69, 932067)-net over F64, using
- net defined by OOA [i] based on linear OOA(6469, 932067, F64, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- net defined by OOA [i] based on linear OOA(6469, 932067, F64, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- trace code for nets [i] based on digital (51, 69, 932067)-net over F64, using
- digital (17, 26, 260)-net over F8, using
- (u, u+v)-construction [i] based on
(147, 147+18, 1864648)-Net in Base 8 — Constructive
(147, 165, 1864648)-net in base 8, using
- 81 times duplication [i] based on (146, 164, 1864648)-net in base 8, using
- base change [i] based on digital (105, 123, 1864648)-net over F16, using
- 161 times duplication [i] based on digital (104, 122, 1864648)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (9, 18, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 9, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 9, 257)-net over F256, 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 (9, 18, 514)-net over F16, using
- (u, u+v)-construction [i] based on
- 161 times duplication [i] based on digital (104, 122, 1864648)-net over F16, using
- base change [i] based on digital (105, 123, 1864648)-net over F16, using
(147, 147+18, large)-Net over F8 — Digital
Digital (147, 165, large)-net over F8, using
- t-expansion [i] based on digital (144, 165, large)-net over F8, using
- 3 times m-reduction [i] based on digital (144, 168, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8168, large, F8, 24) (dual of [large, large−168, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8168, large, F8, 24) (dual of [large, large−168, 25]-code), using
- 3 times m-reduction [i] based on digital (144, 168, large)-net over F8, using
(147, 147+18, large)-Net in Base 8 — Upper bound on s
There is no (147, 165, large)-net in base 8, because
- 16 times m-reduction [i] would yield (147, 149, large)-net in base 8, but