Best Known (86−14, 86, s)-Nets in Base 8
(86−14, 86, 299595)-Net over F8 — Constructive and digital
Digital (72, 86, 299595)-net over F8, using
- net defined by OOA [i] based on linear OOA(886, 299595, F8, 14, 14) (dual of [(299595, 14), 4194244, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(886, 2097165, F8, 14) (dual of [2097165, 2097079, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(886, 2097167, F8, 14) (dual of [2097167, 2097081, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [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(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(886, 2097167, F8, 14) (dual of [2097167, 2097081, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(886, 2097165, F8, 14) (dual of [2097165, 2097079, 15]-code), using
(86−14, 86, 1884296)-Net over F8 — Digital
Digital (72, 86, 1884296)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(886, 1884296, F8, 14) (dual of [1884296, 1884210, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(886, 2097167, F8, 14) (dual of [2097167, 2097081, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [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(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(886, 2097167, F8, 14) (dual of [2097167, 2097081, 15]-code), using
(86−14, 86, large)-Net in Base 8 — Upper bound on s
There is no (72, 86, large)-net in base 8, because
- 12 times m-reduction [i] would yield (72, 74, large)-net in base 8, but