Best Known (102−18, 102, s)-Nets in Base 16
(102−18, 102, 932067)-Net over F16 — Constructive and digital
Digital (84, 102, 932067)-net over F16, using
- 165 times duplication [i] based on digital (79, 97, 932067)-net over F16, using
- net defined by OOA [i] based on linear OOA(1697, 932067, F16, 18, 18) (dual of [(932067, 18), 16777109, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(1697, large, F16, 18) (dual of [large, large−97, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(1697, large, F16, 18) (dual of [large, large−97, 19]-code), using
- net defined by OOA [i] based on linear OOA(1697, 932067, F16, 18, 18) (dual of [(932067, 18), 16777109, 19]-NRT-code), using
(102−18, 102, large)-Net over F16 — Digital
Digital (84, 102, large)-net over F16, using
- 164 times duplication [i] based on digital (80, 98, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1698, large, F16, 18) (dual of [large, large−98, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(1697, large, F16, 18) (dual of [large, large−97, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 1 times code embedding in larger space [i] based on linear OA(1697, large, F16, 18) (dual of [large, large−97, 19]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1698, large, F16, 18) (dual of [large, large−98, 19]-code), using
(102−18, 102, large)-Net in Base 16 — Upper bound on s
There is no (84, 102, large)-net in base 16, because
- 16 times m-reduction [i] would yield (84, 86, large)-net in base 16, but