Best Known (234−36, 234, s)-Nets in Base 2
(234−36, 234, 624)-Net over F2 — Constructive and digital
Digital (198, 234, 624)-net over F2, using
- trace code for nets [i] based on digital (3, 39, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
(234−36, 234, 2048)-Net over F2 — Digital
Digital (198, 234, 2048)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2234, 2048, F2, 4, 36) (dual of [(2048, 4), 7958, 37]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2234, 8192, F2, 36) (dual of [8192, 7958, 37]-code), using
- 1 times truncation [i] based on linear OA(2235, 8193, F2, 37) (dual of [8193, 7958, 38]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2235, 8193, F2, 37) (dual of [8193, 7958, 38]-code), using
- OOA 4-folding [i] based on linear OA(2234, 8192, F2, 36) (dual of [8192, 7958, 37]-code), using
(234−36, 234, 61849)-Net in Base 2 — Upper bound on s
There is no (198, 234, 61850)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 27613 512324 511284 119238 130919 020794 257993 622561 460945 906635 526589 407156 > 2234 [i]