Best Known (129−22, 129, s)-Nets in Base 16
(129−22, 129, 1525200)-Net over F16 — Constructive and digital
Digital (107, 129, 1525200)-net over F16, using
- 161 times duplication [i] based on digital (106, 128, 1525200)-net over F16, using
- trace code for nets [i] based on digital (42, 64, 762600)-net over F256, using
- net defined by OOA [i] based on linear OOA(25664, 762600, F256, 22, 22) (dual of [(762600, 22), 16777136, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(25664, 8388600, F256, 22) (dual of [8388600, 8388536, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(25664, large, F256, 22) (dual of [large, large−64, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(25664, large, F256, 22) (dual of [large, large−64, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(25664, 8388600, F256, 22) (dual of [8388600, 8388536, 23]-code), using
- net defined by OOA [i] based on linear OOA(25664, 762600, F256, 22, 22) (dual of [(762600, 22), 16777136, 23]-NRT-code), using
- trace code for nets [i] based on digital (42, 64, 762600)-net over F256, using
(129−22, 129, large)-Net over F16 — Digital
Digital (107, 129, large)-net over F16, using
- 162 times duplication [i] based on digital (105, 127, large)-net over F16, using
- t-expansion [i] based on digital (104, 127, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16127, large, F16, 23) (dual of [large, large−127, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16127, large, F16, 23) (dual of [large, large−127, 24]-code), using
- t-expansion [i] based on digital (104, 127, large)-net over F16, using
(129−22, 129, large)-Net in Base 16 — Upper bound on s
There is no (107, 129, large)-net in base 16, because
- 20 times m-reduction [i] would yield (107, 109, large)-net in base 16, but