Best Known (164, 164+18, s)-Nets in Base 4
(164, 164+18, 932143)-Net over F4 — Constructive and digital
Digital (164, 182, 932143)-net over F4, using
- 41 times duplication [i] based on digital (163, 181, 932143)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 24, 76)-net over F4, using
- trace code for nets [i] based on digital (3, 12, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- trace code for nets [i] based on digital (3, 12, 38)-net over F16, using
- digital (139, 157, 932067)-net over F4, using
- net defined by OOA [i] based on linear OOA(4157, 932067, F4, 18, 18) (dual of [(932067, 18), 16777049, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- net defined by OOA [i] based on linear OOA(4157, 932067, F4, 18, 18) (dual of [(932067, 18), 16777049, 19]-NRT-code), using
- digital (15, 24, 76)-net over F4, using
- (u, u+v)-construction [i] based on
(164, 164+18, large)-Net over F4 — Digital
Digital (164, 182, large)-net over F4, using
- 46 times duplication [i] based on digital (158, 176, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4176, large, F4, 18) (dual of [large, large−176, 19]-code), using
- 19 times code embedding in larger space [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 19 times code embedding in larger space [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4176, large, F4, 18) (dual of [large, large−176, 19]-code), using
(164, 164+18, large)-Net in Base 4 — Upper bound on s
There is no (164, 182, large)-net in base 4, because
- 16 times m-reduction [i] would yield (164, 166, large)-net in base 4, but