Best Known (36−14, 36, s)-Nets in Base 16
(36−14, 36, 538)-Net over F16 — Constructive and digital
Digital (22, 36, 538)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- digital (14, 28, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 14, 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, 14, 257)-net over F256, using
- digital (1, 8, 24)-net over F16, using
(36−14, 36, 831)-Net over F16 — Digital
Digital (22, 36, 831)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1636, 831, F16, 14) (dual of [831, 795, 15]-code), using
- 185 step Varšamov–Edel lengthening with (ri) = (2, 10 times 0, 1, 51 times 0, 1, 121 times 0) [i] based on linear OA(1632, 642, F16, 14) (dual of [642, 610, 15]-code), using
- trace code [i] based on linear OA(25616, 321, F256, 14) (dual of [321, 305, 15]-code), using
- extended algebraic-geometric code AGe(F,306P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25616, 321, F256, 14) (dual of [321, 305, 15]-code), using
- 185 step Varšamov–Edel lengthening with (ri) = (2, 10 times 0, 1, 51 times 0, 1, 121 times 0) [i] based on linear OA(1632, 642, F16, 14) (dual of [642, 610, 15]-code), using
(36−14, 36, 351107)-Net in Base 16 — Upper bound on s
There is no (22, 36, 351108)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 22 300950 188183 736616 200122 547185 575697 830816 > 1636 [i]