Best Known (122−22, 122, s)-Nets in Base 16
(122−22, 122, 762600)-Net over F16 — Constructive and digital
Digital (100, 122, 762600)-net over F16, using
- 161 times duplication [i] based on digital (99, 121, 762600)-net over F16, using
- net defined by OOA [i] based on linear OOA(16121, 762600, F16, 22, 22) (dual of [(762600, 22), 16777079, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(16121, 8388600, F16, 22) (dual of [8388600, 8388479, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(16121, large, F16, 22) (dual of [large, large−121, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(16121, large, F16, 22) (dual of [large, large−121, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(16121, 8388600, F16, 22) (dual of [8388600, 8388479, 23]-code), using
- net defined by OOA [i] based on linear OOA(16121, 762600, F16, 22, 22) (dual of [(762600, 22), 16777079, 23]-NRT-code), using
(122−22, 122, large)-Net over F16 — Digital
Digital (100, 122, large)-net over F16, using
- 161 times duplication [i] based on digital (99, 121, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16121, large, F16, 22) (dual of [large, large−121, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16121, large, F16, 22) (dual of [large, large−121, 23]-code), using
(122−22, 122, large)-Net in Base 16 — Upper bound on s
There is no (100, 122, large)-net in base 16, because
- 20 times m-reduction [i] would yield (100, 102, large)-net in base 16, but