Best Known (117−19, 117, s)-Nets in Base 16
(117−19, 117, 1864134)-Net over F16 — Constructive and digital
Digital (98, 117, 1864134)-net over F16, using
- 161 times duplication [i] based on digital (97, 116, 1864134)-net over F16, using
- trace code for nets [i] based on digital (39, 58, 932067)-net over F256, using
- net defined by OOA [i] based on linear OOA(25658, 932067, F256, 21, 19) (dual of [(932067, 21), 19573349, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(25658, 2796202, F256, 3, 19) (dual of [(2796202, 3), 8388548, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25655, 2796201, F256, 3, 19) (dual of [(2796201, 3), 8388548, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- OOA 3-folding [i] based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25655, 2796201, F256, 3, 19) (dual of [(2796201, 3), 8388548, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(25658, 2796202, F256, 3, 19) (dual of [(2796202, 3), 8388548, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(25658, 932067, F256, 21, 19) (dual of [(932067, 21), 19573349, 20]-NRT-code), using
- trace code for nets [i] based on digital (39, 58, 932067)-net over F256, using
(117−19, 117, large)-Net over F16 — Digital
Digital (98, 117, large)-net over F16, using
- 162 times duplication [i] based on digital (96, 115, large)-net over F16, using
- t-expansion [i] based on digital (94, 115, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16115, large, F16, 21) (dual of [large, large−115, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16115, large, F16, 21) (dual of [large, large−115, 22]-code), using
- t-expansion [i] based on digital (94, 115, large)-net over F16, using
(117−19, 117, large)-Net in Base 16 — Upper bound on s
There is no (98, 117, large)-net in base 16, because
- 17 times m-reduction [i] would yield (98, 100, large)-net in base 16, but