Best Known (193, 193+43, s)-Nets in Base 4
(193, 193+43, 1549)-Net over F4 — Constructive and digital
Digital (193, 236, 1549)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (2, 23, 10)-net over F4, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 2 and N(F) ≥ 10, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- digital (170, 213, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 71, 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, 71, 513)-net over F64, using
- digital (2, 23, 10)-net over F4, using
(193, 193+43, 15159)-Net over F4 — Digital
Digital (193, 236, 15159)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4236, 15159, F4, 43) (dual of [15159, 14923, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(4236, 16430, F4, 43) (dual of [16430, 16194, 44]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4235, 16429, F4, 43) (dual of [16429, 16194, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(36) [i] based on
- linear OA(4225, 16384, F4, 43) (dual of [16384, 16159, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(42) ⊂ Ce(36) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4235, 16429, F4, 43) (dual of [16429, 16194, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(4236, 16430, F4, 43) (dual of [16430, 16194, 44]-code), using
(193, 193+43, large)-Net in Base 4 — Upper bound on s
There is no (193, 236, large)-net in base 4, because
- 41 times m-reduction [i] would yield (193, 195, large)-net in base 4, but