Best Known (150−31, 150, s)-Nets in Base 8
(150−31, 150, 2188)-Net over F8 — Constructive and digital
Digital (119, 150, 2188)-net over F8, using
- net defined by OOA [i] based on linear OOA(8150, 2188, F8, 31, 31) (dual of [(2188, 31), 67678, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8150, 32821, F8, 31) (dual of [32821, 32671, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(8150, 32822, F8, 31) (dual of [32822, 32672, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(21) [i] based on
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(814, 54, F8, 8) (dual of [54, 40, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(814, 63, F8, 8) (dual of [63, 49, 9]-code), using
- construction X applied to Ce(30) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8150, 32822, F8, 31) (dual of [32822, 32672, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8150, 32821, F8, 31) (dual of [32821, 32671, 32]-code), using
(150−31, 150, 56397)-Net over F8 — Digital
Digital (119, 150, 56397)-net over F8, using
(150−31, 150, large)-Net in Base 8 — Upper bound on s
There is no (119, 150, large)-net in base 8, because
- 29 times m-reduction [i] would yield (119, 121, large)-net in base 8, but