Best Known (146, 146+17, s)-Nets in Base 8
(146, 146+17, 2099200)-Net over F8 — Constructive and digital
Digital (146, 163, 2099200)-net over F8, using
- 81 times duplication [i] based on digital (145, 162, 2099200)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (24, 32, 2050)-net over F8, using
- net defined by OOA [i] based on linear OOA(832, 2050, F8, 8, 8) (dual of [(2050, 8), 16368, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(832, 8200, F8, 8) (dual of [8200, 8168, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(832, 8202, F8, 8) (dual of [8202, 8170, 9]-code), using
- trace code [i] based on linear OA(6416, 4101, F64, 8) (dual of [4101, 4085, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6411, 4096, F64, 6) (dual of [4096, 4085, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(6416, 4101, F64, 8) (dual of [4101, 4085, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(832, 8202, F8, 8) (dual of [8202, 8170, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(832, 8200, F8, 8) (dual of [8200, 8168, 9]-code), using
- net defined by OOA [i] based on linear OOA(832, 2050, F8, 8, 8) (dual of [(2050, 8), 16368, 9]-NRT-code), using
- digital (113, 130, 2097150)-net over F8, using
- net defined by OOA [i] based on linear OOA(8130, 2097150, F8, 18, 17) (dual of [(2097150, 18), 37748570, 18]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(8130, 8388601, F8, 2, 17) (dual of [(8388601, 2), 16777072, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8130, 8388602, F8, 2, 17) (dual of [(8388602, 2), 16777074, 18]-NRT-code), using
- trace code [i] based on linear OOA(6465, 4194301, F64, 2, 17) (dual of [(4194301, 2), 8388537, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6465, 8388602, F64, 17) (dual of [8388602, 8388537, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- OOA 2-folding [i] based on linear OA(6465, 8388602, F64, 17) (dual of [8388602, 8388537, 18]-code), using
- trace code [i] based on linear OOA(6465, 4194301, F64, 2, 17) (dual of [(4194301, 2), 8388537, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8130, 8388602, F8, 2, 17) (dual of [(8388602, 2), 16777074, 18]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(8130, 8388601, F8, 2, 17) (dual of [(8388601, 2), 16777072, 18]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8130, 2097150, F8, 18, 17) (dual of [(2097150, 18), 37748570, 18]-NRT-code), using
- digital (24, 32, 2050)-net over F8, using
- (u, u+v)-construction [i] based on
(146, 146+17, large)-Net over F8 — Digital
Digital (146, 163, large)-net over F8, using
- t-expansion [i] based on digital (144, 163, large)-net over F8, using
- 5 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
- 5 times m-reduction [i] based on digital (144, 168, large)-net over F8, using
(146, 146+17, large)-Net in Base 8 — Upper bound on s
There is no (146, 163, large)-net in base 8, because
- 15 times m-reduction [i] would yield (146, 148, large)-net in base 8, but