Best Known (119, 145, s)-Nets in Base 8
(119, 145, 20168)-Net over F8 — Constructive and digital
Digital (119, 145, 20168)-net over F8, using
- 82 times duplication [i] based on digital (117, 143, 20168)-net over F8, using
- net defined by OOA [i] based on linear OOA(8143, 20168, F8, 26, 26) (dual of [(20168, 26), 524225, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8143, 262184, F8, 26) (dual of [262184, 262041, 27]-code), using
- 3 times code embedding in larger space [i] based on linear OA(8140, 262181, F8, 26) (dual of [262181, 262041, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(8133, 262144, F8, 26) (dual of [262144, 262011, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8103, 262144, F8, 20) (dual of [262144, 262041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(25) ⊂ Ce(19) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(8140, 262181, F8, 26) (dual of [262181, 262041, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8143, 262184, F8, 26) (dual of [262184, 262041, 27]-code), using
- net defined by OOA [i] based on linear OOA(8143, 20168, F8, 26, 26) (dual of [(20168, 26), 524225, 27]-NRT-code), using
(119, 145, 262198)-Net over F8 — Digital
Digital (119, 145, 262198)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8145, 262198, F8, 26) (dual of [262198, 262053, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(8133, 262144, F8, 26) (dual of [262144, 262011, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(891, 262144, F8, 18) (dual of [262144, 262053, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(812, 54, F8, 7) (dual of [54, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(812, 73, F8, 7) (dual of [73, 61, 8]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(812, 73, F8, 7) (dual of [73, 61, 8]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
(119, 145, large)-Net in Base 8 — Upper bound on s
There is no (119, 145, large)-net in base 8, because
- 24 times m-reduction [i] would yield (119, 121, large)-net in base 8, but