Best Known (154, 154+18, s)-Nets in Base 8
(154, 154+18, 1866182)-Net over F8 — Constructive and digital
Digital (154, 172, 1866182)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (25, 34, 2048)-net over F8, using
- net defined by OOA [i] based on linear OOA(834, 2048, F8, 9, 9) (dual of [(2048, 9), 18398, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(834, 8193, F8, 9) (dual of [8193, 8159, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(834, 8194, F8, 9) (dual of [8194, 8160, 10]-code), using
- trace code [i] based on linear OA(6417, 4097, F64, 9) (dual of [4097, 4080, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- trace code [i] based on linear OA(6417, 4097, F64, 9) (dual of [4097, 4080, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(834, 8194, F8, 9) (dual of [8194, 8160, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(834, 8193, F8, 9) (dual of [8193, 8159, 10]-code), using
- net defined by OOA [i] based on linear OOA(834, 2048, F8, 9, 9) (dual of [(2048, 9), 18398, 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 (25, 34, 2048)-net over F8, using
(154, 154+18, large)-Net over F8 — Digital
Digital (154, 172, large)-net over F8, using
- 84 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
(154, 154+18, large)-Net in Base 8 — Upper bound on s
There is no (154, 172, large)-net in base 8, because
- 16 times m-reduction [i] would yield (154, 156, large)-net in base 8, but