Best Known (136, 172, s)-Nets in Base 8
(136, 172, 1824)-Net over F8 — Constructive and digital
Digital (136, 172, 1824)-net over F8, using
- net defined by OOA [i] based on linear OOA(8172, 1824, F8, 36, 36) (dual of [(1824, 36), 65492, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(8172, 32832, F8, 36) (dual of [32832, 32660, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(8172, 32833, F8, 36) (dual of [32833, 32661, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(24) [i] based on
- linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(816, 65, F8, 10) (dual of [65, 49, 11]-code), using
- construction X applied to Ce(35) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(8172, 32833, F8, 36) (dual of [32833, 32661, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(8172, 32832, F8, 36) (dual of [32832, 32660, 37]-code), using
(136, 172, 54494)-Net over F8 — Digital
Digital (136, 172, 54494)-net over F8, using
(136, 172, large)-Net in Base 8 — Upper bound on s
There is no (136, 172, large)-net in base 8, because
- 34 times m-reduction [i] would yield (136, 138, large)-net in base 8, but