Best Known (170−18, 170, s)-Nets in Base 8
(170−18, 170, 1865160)-Net over F8 — Constructive and digital
Digital (152, 170, 1865160)-net over F8, using
- 81 times duplication [i] based on digital (151, 169, 1865160)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (22, 31, 1026)-net over F8, using
- net defined by OOA [i] based on linear OOA(831, 1026, F8, 9, 9) (dual of [(1026, 9), 9203, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(831, 4105, F8, 9) (dual of [4105, 4074, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(829, 4096, F8, 9) (dual of [4096, 4067, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(821, 4096, F8, 6) (dual of [4096, 4075, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [i]
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(831, 4105, F8, 9) (dual of [4105, 4074, 10]-code), using
- net defined by OOA [i] based on linear OOA(831, 1026, F8, 9, 9) (dual of [(1026, 9), 9203, 10]-NRT-code), 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 (22, 31, 1026)-net over F8, using
- (u, u+v)-construction [i] based on
(170−18, 170, large)-Net over F8 — Digital
Digital (152, 170, large)-net over F8, using
- 82 times duplication [i] based on digital (150, 168, large)-net over F8, using
- t-expansion [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
- t-expansion [i] based on digital (144, 168, large)-net over F8, using
(170−18, 170, large)-Net in Base 8 — Upper bound on s
There is no (152, 170, large)-net in base 8, because
- 16 times m-reduction [i] would yield (152, 154, large)-net in base 8, but