Best Known (154−27, 154, s)-Nets in Base 4
(154−27, 154, 1272)-Net over F4 — Constructive and digital
Digital (127, 154, 1272)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (29, 42, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 14, 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, 14, 80)-net over F64, using
- digital (85, 112, 1032)-net over F4, using
- trace code for nets [i] based on digital (1, 28, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 28, 258)-net over F256, using
- digital (29, 42, 240)-net over F4, using
(154−27, 154, 16390)-Net over F4 — Digital
Digital (127, 154, 16390)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4154, 16390, F4, 27) (dual of [16390, 16236, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4154, 16432, F4, 27) (dual of [16432, 16278, 28]-code), using
- 3 times code embedding in larger space [i] based on linear OA(4151, 16429, F4, 27) (dual of [16429, 16278, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(4141, 16384, F4, 27) (dual of [16384, 16243, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(26) ⊂ Ce(20) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(4151, 16429, F4, 27) (dual of [16429, 16278, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4154, 16432, F4, 27) (dual of [16432, 16278, 28]-code), using
(154−27, 154, large)-Net in Base 4 — Upper bound on s
There is no (127, 154, large)-net in base 4, because
- 25 times m-reduction [i] would yield (127, 129, large)-net in base 4, but