Best Known (204, 204+48, s)-Nets in Base 4
(204, 204+48, 1544)-Net over F4 — Constructive and digital
Digital (204, 252, 1544)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 24, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (180, 228, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 76, 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, 76, 513)-net over F64, using
- digital (0, 24, 5)-net over F4, using
(204, 204+48, 11531)-Net over F4 — Digital
Digital (204, 252, 11531)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4252, 11531, F4, 48) (dual of [11531, 11279, 49]-code), using
- discarding factors / shortening the dual code based on linear OA(4252, 16384, F4, 48) (dual of [16384, 16132, 49]-code), using
- 1 times truncation [i] based on linear OA(4253, 16385, F4, 49) (dual of [16385, 16132, 50]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4253, 16385, F4, 49) (dual of [16385, 16132, 50]-code), using
- discarding factors / shortening the dual code based on linear OA(4252, 16384, F4, 48) (dual of [16384, 16132, 49]-code), using
(204, 204+48, 6852833)-Net in Base 4 — Upper bound on s
There is no (204, 252, 6852834)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 52 374415 009686 871431 298603 284367 213741 532882 145201 701308 826787 139305 596002 601966 517509 788665 368407 946183 052277 369383 344254 479142 063547 122640 550868 326196 > 4252 [i]