Best Known (135, 153, s)-Nets in Base 8
(135, 153, 1864162)-Net over F8 — Constructive and digital
Digital (135, 153, 1864162)-net over F8, using
- 81 times duplication [i] based on digital (134, 152, 1864162)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 14, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- 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 (5, 14, 28)-net over F8, using
- (u, u+v)-construction [i] based on
(135, 153, 1864167)-Net in Base 8 — Constructive
(135, 153, 1864167)-net in base 8, using
- (u, u+v)-construction [i] based on
- (6, 15, 33)-net in base 8, using
- 1 times m-reduction [i] based on (6, 16, 33)-net in base 8, using
- base change [i] based on digital (2, 12, 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
- base change [i] based on digital (2, 12, 33)-net over F16, using
- 1 times m-reduction [i] based on (6, 16, 33)-net in base 8, using
- 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
- (6, 15, 33)-net in base 8, using
(135, 153, large)-Net over F8 — Digital
Digital (135, 153, large)-net over F8, using
- t-expansion [i] based on digital (131, 153, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8153, large, F8, 22) (dual of [large, large−153, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, 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(8153, large, F8, 22) (dual of [large, large−153, 23]-code), using
(135, 153, large)-Net in Base 8 — Upper bound on s
There is no (135, 153, large)-net in base 8, because
- 16 times m-reduction [i] would yield (135, 137, large)-net in base 8, but