Best Known (209, 256, s)-Nets in Base 4
(209, 256, 1560)-Net over F4 — Constructive and digital
Digital (209, 256, 1560)-net over F4, using
- 41 times duplication [i] based on digital (208, 255, 1560)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (7, 30, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- digital (178, 225, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 75, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 75, 513)-net over F64, using
- digital (7, 30, 21)-net over F4, using
- (u, u+v)-construction [i] based on
(209, 256, 15125)-Net over F4 — Digital
Digital (209, 256, 15125)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4256, 15125, F4, 47) (dual of [15125, 14869, 48]-code), using
- discarding factors / shortening the dual code based on linear OA(4256, 16429, F4, 47) (dual of [16429, 16173, 48]-code), using
- construction X applied to Ce(46) ⊂ Ce(40) [i] based on
- linear OA(4246, 16384, F4, 47) (dual of [16384, 16138, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(410, 45, F4, 5) (dual of [45, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(46) ⊂ Ce(40) [i] based on
- discarding factors / shortening the dual code based on linear OA(4256, 16429, F4, 47) (dual of [16429, 16173, 48]-code), using
(209, 256, large)-Net in Base 4 — Upper bound on s
There is no (209, 256, large)-net in base 4, because
- 45 times m-reduction [i] would yield (209, 211, large)-net in base 4, but