Best Known (17, 17+6, s)-Nets in Base 128
(17, 17+6, 2796201)-Net over F128 — Constructive and digital
Digital (17, 23, 2796201)-net over F128, using
- 1282 times duplication [i] based on digital (15, 21, 2796201)-net over F128, using
- net defined by OOA [i] based on linear OOA(12821, 2796201, F128, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(12821, large, F128, 6) (dual of [large, large−21, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(12821, large, F128, 6) (dual of [large, large−21, 7]-code), using
- net defined by OOA [i] based on linear OOA(12821, 2796201, F128, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
(17, 17+6, 2861737)-Net in Base 128 — Constructive
(17, 23, 2861737)-net in base 128, using
- net defined by OOA [i] based on OOA(12823, 2861737, S128, 9, 6), using
- OOA stacking with additional row [i] based on OOA(12823, 2861738, S128, 3, 6), using
- discarding parts of the base [i] based on linear OOA(25620, 2861738, F256, 3, 6) (dual of [(2861738, 3), 8585194, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2564, 65537, F256, 3, 3) (dual of [(65537, 3), 196607, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(2564, 65537, F256, 2, 3) (dual of [(65537, 2), 131070, 4]-NRT-code), using
- linear OOA(25616, 2796201, F256, 3, 6) (dual of [(2796201, 3), 8388587, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- linear OOA(2564, 65537, F256, 3, 3) (dual of [(65537, 3), 196607, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding parts of the base [i] based on linear OOA(25620, 2861738, F256, 3, 6) (dual of [(2861738, 3), 8585194, 7]-NRT-code), using
- OOA stacking with additional row [i] based on OOA(12823, 2861738, S128, 3, 6), using
(17, 17+6, large)-Net over F128 — Digital
Digital (17, 23, large)-net over F128, using
- 1282 times duplication [i] based on digital (15, 21, large)-net over F128, using
(17, 17+6, large)-Net in Base 128 — Upper bound on s
There is no (17, 23, large)-net in base 128, because
- 4 times m-reduction [i] would yield (17, 19, large)-net in base 128, but