Best Known (170, 204, s)-Nets in Base 2
(170, 204, 390)-Net over F2 — Constructive and digital
Digital (170, 204, 390)-net over F2, using
- trace code for nets [i] based on digital (0, 34, 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
(170, 204, 1209)-Net over F2 — Digital
Digital (170, 204, 1209)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2204, 1209, F2, 3, 34) (dual of [(1209, 3), 3423, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2204, 1365, F2, 3, 34) (dual of [(1365, 3), 3891, 35]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2204, 4095, F2, 34) (dual of [4095, 3891, 35]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using
- OOA 3-folding [i] based on linear OA(2204, 4095, F2, 34) (dual of [4095, 3891, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(2204, 1365, F2, 3, 34) (dual of [(1365, 3), 3891, 35]-NRT-code), using
(170, 204, 29372)-Net in Base 2 — Upper bound on s
There is no (170, 204, 29373)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 25 723580 262600 490405 094497 311764 891500 428663 100515 066805 537478 > 2204 [i]