Best Known (169−49, 169, s)-Nets in Base 8
(169−49, 169, 1026)-Net over F8 — Constructive and digital
Digital (120, 169, 1026)-net over F8, using
- t-expansion [i] based on digital (114, 169, 1026)-net over F8, using
- 3 times m-reduction [i] based on digital (114, 172, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 86, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 86, 513)-net over F64, using
- 3 times m-reduction [i] based on digital (114, 172, 1026)-net over F8, using
(169−49, 169, 4097)-Net over F8 — Digital
Digital (120, 169, 4097)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8169, 4097, F8, 49) (dual of [4097, 3928, 50]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
(169−49, 169, 2936921)-Net in Base 8 — Upper bound on s
There is no (120, 169, 2936922)-net in base 8, because
- 1 times m-reduction [i] would yield (120, 168, 2936922)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 52 374292 720229 785730 545653 263157 837963 143024 153762 495046 307466 740522 184033 867483 389791 147961 464630 597641 438421 257995 928407 227272 037206 042637 572246 289197 > 8168 [i]