Best Known (160−28, 160, s)-Nets in Base 4
(160−28, 160, 1268)-Net over F4 — Constructive and digital
Digital (132, 160, 1268)-net over F4, using
- 1 times m-reduction [i] based on digital (132, 161, 1268)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (31, 45, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 15, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 15, 80)-net over F64, using
- digital (87, 116, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 29, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 29, 257)-net over F256, using
- digital (31, 45, 240)-net over F4, using
- (u, u+v)-construction [i] based on
(160−28, 160, 16433)-Net over F4 — Digital
Digital (132, 160, 16433)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4160, 16433, F4, 28) (dual of [16433, 16273, 29]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4157, 16428, F4, 28) (dual of [16428, 16271, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(49, 44, F4, 5) (dual of [44, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(4157, 16430, F4, 26) (dual of [16430, 16273, 27]-code), using Gilbert–Varšamov bound and bm = 4157 > Vbs−1(k−1) = 131 810576 289040 175058 322088 251088 002285 240290 929852 635932 974484 216571 335842 766915 721909 205392 [i]
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(4157, 16428, F4, 28) (dual of [16428, 16271, 29]-code), using
- construction X with Varšamov bound [i] based on
(160−28, 160, large)-Net in Base 4 — Upper bound on s
There is no (132, 160, large)-net in base 4, because
- 26 times m-reduction [i] would yield (132, 134, large)-net in base 4, but