Best Known (203−18, 203, s)-Nets in Base 4
(203−18, 203, 1864139)-Net over F4 — Constructive and digital
Digital (185, 203, 1864139)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (176, 194, 1864134)-net over F4, using
- trace code for nets [i] based on digital (79, 97, 932067)-net over F16, using
- net defined by OOA [i] based on linear OOA(1697, 932067, F16, 18, 18) (dual of [(932067, 18), 16777109, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(1697, large, F16, 18) (dual of [large, large−97, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(1697, large, F16, 18) (dual of [large, large−97, 19]-code), using
- net defined by OOA [i] based on linear OOA(1697, 932067, F16, 18, 18) (dual of [(932067, 18), 16777109, 19]-NRT-code), using
- trace code for nets [i] based on digital (79, 97, 932067)-net over F16, using
- digital (0, 9, 5)-net over F4, using
(203−18, 203, large)-Net over F4 — Digital
Digital (185, 203, large)-net over F4, using
- 46 times duplication [i] based on digital (179, 197, large)-net over F4, using
- t-expansion [i] based on digital (177, 197, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4197, large, F4, 20) (dual of [large, large−197, 21]-code), using
- 17 times code embedding in larger space [i] based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 17 times code embedding in larger space [i] based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4197, large, F4, 20) (dual of [large, large−197, 21]-code), using
- t-expansion [i] based on digital (177, 197, large)-net over F4, using
(203−18, 203, large)-Net in Base 4 — Upper bound on s
There is no (185, 203, large)-net in base 4, because
- 16 times m-reduction [i] would yield (185, 187, large)-net in base 4, but