Best Known (92−18, 92, s)-Nets in Base 8
(92−18, 92, 29127)-Net over F8 — Constructive and digital
Digital (74, 92, 29127)-net over F8, using
- 81 times duplication [i] based on digital (73, 91, 29127)-net over F8, using
- net defined by OOA [i] based on linear OOA(891, 29127, F8, 18, 18) (dual of [(29127, 18), 524195, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(891, 262143, F8, 18) (dual of [262143, 262052, 19]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(891, 262144, F8, 18) (dual of [262144, 262053, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(891, 262143, F8, 18) (dual of [262143, 262052, 19]-code), using
- net defined by OOA [i] based on linear OOA(891, 29127, F8, 18, 18) (dual of [(29127, 18), 524195, 19]-NRT-code), using
(92−18, 92, 132964)-Net over F8 — Digital
Digital (74, 92, 132964)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(892, 132964, F8, 18) (dual of [132964, 132872, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(892, 262151, F8, 18) (dual of [262151, 262059, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(891, 262150, F8, 18) (dual of [262150, 262059, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- 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(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(80, 6, F8, 0) (dual of [6, 6, 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(17) ⊂ Ce(16) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(891, 262150, F8, 18) (dual of [262150, 262059, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(892, 262151, F8, 18) (dual of [262151, 262059, 19]-code), using
(92−18, 92, large)-Net in Base 8 — Upper bound on s
There is no (74, 92, large)-net in base 8, because
- 16 times m-reduction [i] would yield (74, 76, large)-net in base 8, but