Best Known (110−18, 110, s)-Nets in Base 8
(110−18, 110, 233019)-Net over F8 — Constructive and digital
Digital (92, 110, 233019)-net over F8, using
- net defined by OOA [i] based on linear OOA(8110, 233019, F8, 18, 18) (dual of [(233019, 18), 4194232, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(8110, 2097171, F8, 18) (dual of [2097171, 2097061, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(8110, 2097177, F8, 18) (dual of [2097177, 2097067, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(84, 25, F8, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,8)), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(8110, 2097177, F8, 18) (dual of [2097177, 2097067, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(8110, 2097171, F8, 18) (dual of [2097171, 2097061, 19]-code), using
(110−18, 110, 1379553)-Net over F8 — Digital
Digital (92, 110, 1379553)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8110, 1379553, F8, 18) (dual of [1379553, 1379443, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(8110, 2097177, F8, 18) (dual of [2097177, 2097067, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(84, 25, F8, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,8)), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(8110, 2097177, F8, 18) (dual of [2097177, 2097067, 19]-code), using
(110−18, 110, large)-Net in Base 8 — Upper bound on s
There is no (92, 110, large)-net in base 8, because
- 16 times m-reduction [i] would yield (92, 94, large)-net in base 8, but