Best Known (186, 186+18, s)-Nets in Base 4
(186, 186+18, 1864143)-Net over F4 — Constructive and digital
Digital (186, 204, 1864143)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 9)-net over F4, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- net from sequence [i] based on digital (1, 8)-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 (1, 10, 9)-net over F4, using
(186, 186+18, large)-Net over F4 — Digital
Digital (186, 204, large)-net over F4, using
- 3 times m-reduction [i] based on digital (186, 207, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4207, large, F4, 21) (dual of [large, large−207, 22]-code), using
- 26 times code embedding in larger space [i] based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 26 times code embedding in larger space [i] based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4207, large, F4, 21) (dual of [large, large−207, 22]-code), using
(186, 186+18, large)-Net in Base 4 — Upper bound on s
There is no (186, 204, large)-net in base 4, because
- 16 times m-reduction [i] would yield (186, 188, large)-net in base 4, but