Best Known (60−24, 60, s)-Nets in Base 16
(60−24, 60, 531)-Net over F16 — Constructive and digital
Digital (36, 60, 531)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (24, 48, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 24, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 24, 257)-net over F256, using
- digital (0, 12, 17)-net over F16, using
(60−24, 60, 883)-Net over F16 — Digital
Digital (36, 60, 883)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1660, 883, F16, 24) (dual of [883, 823, 25]-code), using
- 233 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 6 times 0, 1, 19 times 0, 1, 39 times 0, 1, 69 times 0, 1, 92 times 0) [i] based on linear OA(1652, 642, F16, 24) (dual of [642, 590, 25]-code), using
- trace code [i] based on linear OA(25626, 321, F256, 24) (dual of [321, 295, 25]-code), using
- extended algebraic-geometric code AGe(F,296P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25626, 321, F256, 24) (dual of [321, 295, 25]-code), using
- 233 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 6 times 0, 1, 19 times 0, 1, 39 times 0, 1, 69 times 0, 1, 92 times 0) [i] based on linear OA(1652, 642, F16, 24) (dual of [642, 590, 25]-code), using
(60−24, 60, 369711)-Net in Base 16 — Upper bound on s
There is no (36, 60, 369712)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 766890 002810 686676 032036 142856 323306 255296 343806 139405 047439 055335 720211 > 1660 [i]