Best Known (89−14, 89, s)-Nets in Base 8
(89−14, 89, 299597)-Net over F8 — Constructive and digital
Digital (75, 89, 299597)-net over F8, using
- net defined by OOA [i] based on linear OOA(889, 299597, F8, 14, 14) (dual of [(299597, 14), 4194269, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(889, 2097179, F8, 14) (dual of [2097179, 2097090, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(889, 2097184, F8, 14) (dual of [2097184, 2097095, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- 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(857, 2097152, F8, 10) (dual of [2097152, 2097095, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(889, 2097184, F8, 14) (dual of [2097184, 2097095, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(889, 2097179, F8, 14) (dual of [2097179, 2097090, 15]-code), using
(89−14, 89, 2097184)-Net over F8 — Digital
Digital (75, 89, 2097184)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(889, 2097184, F8, 14) (dual of [2097184, 2097095, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- 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(857, 2097152, F8, 10) (dual of [2097152, 2097095, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
(89−14, 89, large)-Net in Base 8 — Upper bound on s
There is no (75, 89, large)-net in base 8, because
- 12 times m-reduction [i] would yield (75, 77, large)-net in base 8, but