Best Known (147−34, 147, s)-Nets in Base 8
(147−34, 147, 1927)-Net over F8 — Constructive and digital
Digital (113, 147, 1927)-net over F8, using
- 81 times duplication [i] based on digital (112, 146, 1927)-net over F8, using
- net defined by OOA [i] based on linear OOA(8146, 1927, F8, 34, 34) (dual of [(1927, 34), 65372, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(8146, 32759, F8, 34) (dual of [32759, 32613, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(8146, 32759, F8, 34) (dual of [32759, 32613, 35]-code), using
- net defined by OOA [i] based on linear OOA(8146, 1927, F8, 34, 34) (dual of [(1927, 34), 65372, 35]-NRT-code), using
(147−34, 147, 24087)-Net over F8 — Digital
Digital (113, 147, 24087)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8147, 24087, F8, 34) (dual of [24087, 23940, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8147, 32774, F8, 34) (dual of [32774, 32627, 35]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8146, 32773, F8, 34) (dual of [32773, 32627, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(8146, 32773, F8, 34) (dual of [32773, 32627, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8147, 32774, F8, 34) (dual of [32774, 32627, 35]-code), using
(147−34, 147, large)-Net in Base 8 — Upper bound on s
There is no (113, 147, large)-net in base 8, because
- 32 times m-reduction [i] would yield (113, 115, large)-net in base 8, but