Best Known (128, 155, s)-Nets in Base 4
(128, 155, 1272)-Net over F4 — Constructive and digital
Digital (128, 155, 1272)-net over F4, using
- 41 times duplication [i] based on 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
- (u, u+v)-construction [i] based on
(128, 155, 16441)-Net over F4 — Digital
Digital (128, 155, 16441)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4155, 16441, F4, 27) (dual of [16441, 16286, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,9]) [i] based on
- linear OA(4141, 16385, F4, 27) (dual of [16385, 16244, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(499, 16385, F4, 19) (dual of [16385, 16286, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to C([0,13]) ⊂ C([0,9]) [i] based on
(128, 155, large)-Net in Base 4 — Upper bound on s
There is no (128, 155, large)-net in base 4, because
- 25 times m-reduction [i] would yield (128, 130, large)-net in base 4, but