Best Known (81−35, 81, s)-Nets in Base 16
(81−35, 81, 524)-Net over F16 — Constructive and digital
Digital (46, 81, 524)-net over F16, using
- 1 times m-reduction [i] based on digital (46, 82, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 41, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 41, 262)-net over F256, using
(81−35, 81, 699)-Net over F16 — Digital
Digital (46, 81, 699)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1681, 699, F16, 35) (dual of [699, 618, 36]-code), using
- 50 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 13 times 0, 1, 27 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
- 50 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 13 times 0, 1, 27 times 0) [i] based on linear OA(1674, 642, F16, 35) (dual of [642, 568, 36]-code), using
(81−35, 81, 221964)-Net in Base 16 — Upper bound on s
There is no (46, 81, 221965)-net in base 16, because
- 1 times m-reduction [i] would yield (46, 80, 221965)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 2 136107 765917 643962 294292 276527 732875 825154 088854 712153 209148 259584 764559 160374 874025 490687 920576 > 1680 [i]