Best Known (132−22, 132, s)-Nets in Base 2
(132−22, 132, 390)-Net over F2 — Constructive and digital
Digital (110, 132, 390)-net over F2, using
- trace code for nets [i] based on digital (0, 22, 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
(132−22, 132, 1059)-Net over F2 — Digital
Digital (110, 132, 1059)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2132, 1059, F2, 3, 22) (dual of [(1059, 3), 3045, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2132, 1365, F2, 3, 22) (dual of [(1365, 3), 3963, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2132, 4095, F2, 22) (dual of [4095, 3963, 23]-code), using
- 1 times truncation [i] based on linear OA(2133, 4096, F2, 23) (dual of [4096, 3963, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 1 times truncation [i] based on linear OA(2133, 4096, F2, 23) (dual of [4096, 3963, 24]-code), using
- OOA 3-folding [i] based on linear OA(2132, 4095, F2, 22) (dual of [4095, 3963, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(2132, 1365, F2, 3, 22) (dual of [(1365, 3), 3963, 23]-NRT-code), using
(132−22, 132, 20092)-Net in Base 2 — Upper bound on s
There is no (110, 132, 20093)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 5446 758742 853518 898372 934538 331052 983776 > 2132 [i]