Best Known (47, 82, s)-Nets in Base 16
(47, 82, 526)-Net over F16 — Constructive and digital
Digital (47, 82, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 41, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(47, 82, 745)-Net over F16 — Digital
Digital (47, 82, 745)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1682, 745, F16, 35) (dual of [745, 663, 36]-code), using
- 95 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 13 times 0, 1, 27 times 0, 1, 44 times 0) [i] based on linear OA(1674, 642, F16, 35) (dual of [642, 568, 36]-code), using
- trace code [i] based on linear OA(25637, 321, F256, 35) (dual of [321, 284, 36]-code), using
- extended algebraic-geometric code AGe(F,285P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25637, 321, F256, 35) (dual of [321, 284, 36]-code), using
- 95 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 13 times 0, 1, 27 times 0, 1, 44 times 0) [i] based on linear OA(1674, 642, F16, 35) (dual of [642, 568, 36]-code), using
(47, 82, 261286)-Net in Base 16 — Upper bound on s
There is no (47, 82, 261287)-net in base 16, because
- 1 times m-reduction [i] would yield (47, 81, 261287)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 34 177760 229834 966359 264138 368302 274864 215594 847970 961741 265441 123933 947280 321997 745778 776261 026236 > 1681 [i]