Best Known (108−19, 108, s)-Nets in Base 16
(108−19, 108, 932066)-Net over F16 — Constructive and digital
Digital (89, 108, 932066)-net over F16, using
- 165 times duplication [i] based on digital (84, 103, 932066)-net over F16, using
- net defined by OOA [i] based on linear OOA(16103, 932066, F16, 19, 19) (dual of [(932066, 19), 17709151, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(16103, 8388595, F16, 19) (dual of [8388595, 8388492, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(16103, large, F16, 19) (dual of [large, large−103, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(16103, large, F16, 19) (dual of [large, large−103, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(16103, 8388595, F16, 19) (dual of [8388595, 8388492, 20]-code), using
- net defined by OOA [i] based on linear OOA(16103, 932066, F16, 19, 19) (dual of [(932066, 19), 17709151, 20]-NRT-code), using
(108−19, 108, large)-Net over F16 — Digital
Digital (89, 108, large)-net over F16, using
- 1 times m-reduction [i] based on digital (89, 109, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16109, large, F16, 20) (dual of [large, large−109, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16109, large, F16, 20) (dual of [large, large−109, 21]-code), using
(108−19, 108, large)-Net in Base 16 — Upper bound on s
There is no (89, 108, large)-net in base 16, because
- 17 times m-reduction [i] would yield (89, 91, large)-net in base 16, but