Best Known (132, 132+29, s)-Nets in Base 8
(132, 132+29, 18727)-Net over F8 — Constructive and digital
Digital (132, 161, 18727)-net over F8, using
- 83 times duplication [i] based on digital (129, 158, 18727)-net over F8, using
- net defined by OOA [i] based on linear OOA(8158, 18727, F8, 29, 29) (dual of [(18727, 29), 542925, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8158, 262179, F8, 29) (dual of [262179, 262021, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8158, 262181, F8, 29) (dual of [262181, 262023, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- linear OA(8151, 262144, F8, 29) (dual of [262144, 261993, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(87, 37, F8, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(8158, 262181, F8, 29) (dual of [262181, 262023, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8158, 262179, F8, 29) (dual of [262179, 262021, 30]-code), using
- net defined by OOA [i] based on linear OOA(8158, 18727, F8, 29, 29) (dual of [(18727, 29), 542925, 30]-NRT-code), using
(132, 132+29, 262190)-Net over F8 — Digital
Digital (132, 161, 262190)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8161, 262190, F8, 29) (dual of [262190, 262029, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(8151, 262144, F8, 29) (dual of [262144, 261993, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(810, 46, F8, 6) (dual of [46, 36, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
(132, 132+29, large)-Net in Base 8 — Upper bound on s
There is no (132, 161, large)-net in base 8, because
- 27 times m-reduction [i] would yield (132, 134, large)-net in base 8, but