Best Known (142, 170, s)-Nets in Base 2
(142, 170, 390)-Net over F2 — Constructive and digital
Digital (142, 170, 390)-net over F2, using
- 22 times duplication [i] based on digital (140, 168, 390)-net over F2, using
- trace code for nets [i] based on digital (0, 28, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 28, 65)-net over F64, using
(142, 170, 1185)-Net over F2 — Digital
Digital (142, 170, 1185)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2170, 1185, F2, 3, 28) (dual of [(1185, 3), 3385, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2170, 1369, F2, 3, 28) (dual of [(1369, 3), 3937, 29]-NRT-code), using
- strength reduction [i] based on linear OOA(2170, 1369, F2, 3, 29) (dual of [(1369, 3), 3937, 30]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2170, 4107, F2, 29) (dual of [4107, 3937, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2170, 4109, F2, 29) (dual of [4109, 3939, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2169, 4096, F2, 29) (dual of [4096, 3927, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2157, 4096, F2, 27) (dual of [4096, 3939, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(2170, 4109, F2, 29) (dual of [4109, 3939, 30]-code), using
- OOA 3-folding [i] based on linear OA(2170, 4107, F2, 29) (dual of [4107, 3937, 30]-code), using
- strength reduction [i] based on linear OOA(2170, 1369, F2, 3, 29) (dual of [(1369, 3), 3937, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2170, 1369, F2, 3, 28) (dual of [(1369, 3), 3937, 29]-NRT-code), using
(142, 170, 27320)-Net in Base 2 — Upper bound on s
There is no (142, 170, 27321)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1496 589935 339728 980759 684394 132344 742397 118392 547336 > 2170 [i]