Best Known (192−30, 192, s)-Nets in Base 2
(192−30, 192, 490)-Net over F2 — Constructive and digital
Digital (162, 192, 490)-net over F2, using
- 22 times duplication [i] based on digital (160, 190, 490)-net over F2, using
- t-expansion [i] based on digital (159, 190, 490)-net over F2, using
- trace code for nets [i] based on digital (7, 38, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- trace code for nets [i] based on digital (7, 38, 98)-net over F32, using
- t-expansion [i] based on digital (159, 190, 490)-net over F2, using
(192−30, 192, 1396)-Net over F2 — Digital
Digital (162, 192, 1396)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2192, 1396, F2, 2, 30) (dual of [(1396, 2), 2600, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2192, 2071, F2, 2, 30) (dual of [(2071, 2), 3950, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2192, 4142, F2, 30) (dual of [4142, 3950, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2192, 4143, F2, 30) (dual of [4143, 3951, 31]-code), using
- 1 times truncation [i] based on linear OA(2193, 4144, F2, 31) (dual of [4144, 3951, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(30) ⊂ Ce(24) [i] based on
- 1 times truncation [i] based on linear OA(2193, 4144, F2, 31) (dual of [4144, 3951, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2192, 4143, F2, 30) (dual of [4143, 3951, 31]-code), using
- OOA 2-folding [i] based on linear OA(2192, 4142, F2, 30) (dual of [4142, 3950, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(2192, 2071, F2, 2, 30) (dual of [(2071, 2), 3950, 31]-NRT-code), using
(192−30, 192, 45786)-Net in Base 2 — Upper bound on s
There is no (162, 192, 45787)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6277 140913 890574 442624 572776 796347 965634 902218 751261 667848 > 2192 [i]