Best Known (106−17, 106, s)-Nets in Base 8
(106−17, 106, 262149)-Net over F8 — Constructive and digital
Digital (89, 106, 262149)-net over F8, using
- net defined by OOA [i] based on linear OOA(8106, 262149, F8, 17, 17) (dual of [(262149, 17), 4456427, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(8106, 2097193, F8, 17) (dual of [2097193, 2097087, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8106, 2097194, F8, 17) (dual of [2097194, 2097088, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(864, 2097152, F8, 11) (dual of [2097152, 2097088, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(87, 42, F8, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(8106, 2097194, F8, 17) (dual of [2097194, 2097088, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(8106, 2097193, F8, 17) (dual of [2097193, 2097087, 18]-code), using
(106−17, 106, 1924405)-Net over F8 — Digital
Digital (89, 106, 1924405)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8106, 1924405, F8, 17) (dual of [1924405, 1924299, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8106, 2097188, F8, 17) (dual of [2097188, 2097082, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(871, 2097153, F8, 11) (dual of [2097153, 2097082, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(87, 35, F8, 5) (dual of [35, 28, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8106, 2097188, F8, 17) (dual of [2097188, 2097082, 18]-code), using
(106−17, 106, large)-Net in Base 8 — Upper bound on s
There is no (89, 106, large)-net in base 8, because
- 15 times m-reduction [i] would yield (89, 91, large)-net in base 8, but