Best Known (50−21, 50, s)-Nets in Base 16
(50−21, 50, 522)-Net over F16 — Constructive and digital
Digital (29, 50, 522)-net over F16, using
- trace code for nets [i] based on digital (4, 25, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
(50−21, 50, 663)-Net over F16 — Digital
Digital (29, 50, 663)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1650, 663, F16, 21) (dual of [663, 613, 22]-code), using
- 17 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 12 times 0) [i] based on linear OA(1646, 642, F16, 21) (dual of [642, 596, 22]-code), using
- trace code [i] based on linear OA(25623, 321, F256, 21) (dual of [321, 298, 22]-code), using
- extended algebraic-geometric code AGe(F,299P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25623, 321, F256, 21) (dual of [321, 298, 22]-code), using
- 17 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 12 times 0) [i] based on linear OA(1646, 642, F16, 21) (dual of [642, 596, 22]-code), using
(50−21, 50, 239918)-Net in Base 16 — Upper bound on s
There is no (29, 50, 239919)-net in base 16, because
- 1 times m-reduction [i] would yield (29, 49, 239919)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 100436 023000 829894 770894 417616 930564 526463 934887 938503 174101 > 1649 [i]