Best Known (130−56, 130, s)-Nets in Base 16
(130−56, 130, 532)-Net over F16 — Constructive and digital
Digital (74, 130, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 65, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(130−56, 130, 1027)-Net over F16 — Digital
Digital (74, 130, 1027)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(16130, 1027, F16, 2, 56) (dual of [(1027, 2), 1924, 57]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(16128, 1026, F16, 2, 56) (dual of [(1026, 2), 1924, 57]-NRT-code), using
- extracting embedded OOA [i] based on digital (72, 128, 1026)-net over F16, using
- trace code for nets [i] based on digital (8, 64, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- trace code for nets [i] based on digital (8, 64, 513)-net over F256, using
- extracting embedded OOA [i] based on digital (72, 128, 1026)-net over F16, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(16128, 1026, F16, 2, 56) (dual of [(1026, 2), 1924, 57]-NRT-code), using
(130−56, 130, 293391)-Net in Base 16 — Upper bound on s
There is no (74, 130, 293392)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 3 432438 809913 594544 534286 249873 126690 193949 501953 192994 514620 845084 410764 058585 810612 423816 488539 598753 020411 672813 556978 530427 825403 916796 594089 132490 376416 > 16130 [i]