Best Known (138, 168, s)-Nets in Base 8
(138, 168, 17479)-Net over F8 — Constructive and digital
Digital (138, 168, 17479)-net over F8, using
- net defined by OOA [i] based on linear OOA(8168, 17479, F8, 30, 30) (dual of [(17479, 30), 524202, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(8168, 262185, F8, 30) (dual of [262185, 262017, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8168, 262191, F8, 30) (dual of [262191, 262023, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- linear OA(8157, 262144, F8, 30) (dual of [262144, 261987, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8121, 262144, F8, 23) (dual of [262144, 262023, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(811, 47, F8, 6) (dual of [47, 36, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(8168, 262191, F8, 30) (dual of [262191, 262023, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(8168, 262185, F8, 30) (dual of [262185, 262017, 31]-code), using
(138, 168, 284276)-Net over F8 — Digital
Digital (138, 168, 284276)-net over F8, using
(138, 168, large)-Net in Base 8 — Upper bound on s
There is no (138, 168, large)-net in base 8, because
- 28 times m-reduction [i] would yield (138, 140, large)-net in base 8, but