Best Known (106, 106+18, s)-Nets in Base 8
(106, 106+18, 932067)-Net over F8 — Constructive and digital
Digital (106, 124, 932067)-net over F8, using
- 83 times duplication [i] based on digital (103, 121, 932067)-net over F8, using
- net defined by OOA [i] based on linear OOA(8121, 932067, F8, 18, 18) (dual of [(932067, 18), 16777085, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(8121, large, F8, 18) (dual of [large, large−121, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(8121, large, F8, 18) (dual of [large, large−121, 19]-code), using
- net defined by OOA [i] based on linear OOA(8121, 932067, F8, 18, 18) (dual of [(932067, 18), 16777085, 19]-NRT-code), using
(106, 106+18, large)-Net over F8 — Digital
Digital (106, 124, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8124, large, F8, 18) (dual of [large, large−124, 19]-code), using
- 3 times code embedding in larger space [i] based on linear OA(8121, large, F8, 18) (dual of [large, large−121, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 3 times code embedding in larger space [i] based on linear OA(8121, large, F8, 18) (dual of [large, large−121, 19]-code), using
(106, 106+18, large)-Net in Base 8 — Upper bound on s
There is no (106, 124, large)-net in base 8, because
- 16 times m-reduction [i] would yield (106, 108, large)-net in base 8, but