Best Known (184, 218, s)-Nets in Base 2
(184, 218, 520)-Net over F2 — Constructive and digital
Digital (184, 218, 520)-net over F2, using
- 23 times duplication [i] based on digital (181, 215, 520)-net over F2, using
- trace code for nets [i] based on digital (9, 43, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- trace code for nets [i] based on digital (9, 43, 104)-net over F32, using
(184, 218, 1509)-Net over F2 — Digital
Digital (184, 218, 1509)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2218, 1509, F2, 2, 34) (dual of [(1509, 2), 2800, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2218, 2072, F2, 2, 34) (dual of [(2072, 2), 3926, 35]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2217, 2072, F2, 2, 34) (dual of [(2072, 2), 3927, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2217, 4144, F2, 34) (dual of [4144, 3927, 35]-code), using
- strength reduction [i] based on linear OA(2217, 4144, F2, 35) (dual of [4144, 3927, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- 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(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- strength reduction [i] based on linear OA(2217, 4144, F2, 35) (dual of [4144, 3927, 36]-code), using
- OOA 2-folding [i] based on linear OA(2217, 4144, F2, 34) (dual of [4144, 3927, 35]-code), using
- 21 times duplication [i] based on linear OOA(2217, 2072, F2, 2, 34) (dual of [(2072, 2), 3927, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2218, 2072, F2, 2, 34) (dual of [(2072, 2), 3926, 35]-NRT-code), using
(184, 218, 52000)-Net in Base 2 — Upper bound on s
There is no (184, 218, 52001)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 421384 088628 326166 244045 578015 302532 052286 890201 192609 702562 500172 > 2218 [i]