Best Known (106, 106+18, s)-Nets in Base 16
(106, 106+18, 1864650)-Net over F16 — Constructive and digital
Digital (106, 124, 1864650)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (11, 20, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 10, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 10, 258)-net over F256, using
- digital (86, 104, 1864134)-net over F16, using
- trace code for nets [i] based on digital (34, 52, 932067)-net over F256, using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- trace code for nets [i] based on digital (34, 52, 932067)-net over F256, using
- digital (11, 20, 516)-net over F16, using
(106, 106+18, large)-Net over F16 — Digital
Digital (106, 124, large)-net over F16, using
- t-expansion [i] based on digital (104, 124, large)-net over F16, using
- 3 times m-reduction [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
- 3 times m-reduction [i] based on digital (104, 127, large)-net over F16, using
(106, 106+18, large)-Net in Base 16 — Upper bound on s
There is no (106, 124, large)-net in base 16, because
- 16 times m-reduction [i] would yield (106, 108, large)-net in base 16, but