Best Known (50, 89, s)-Nets in Base 16
(50, 89, 524)-Net over F16 — Constructive and digital
Digital (50, 89, 524)-net over F16, using
- 1 times m-reduction [i] based on digital (50, 90, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 45, 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, 45, 262)-net over F256, using
(50, 89, 695)-Net over F16 — Digital
Digital (50, 89, 695)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1689, 695, F16, 39) (dual of [695, 606, 40]-code), using
- 46 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0) [i] based on linear OA(1682, 642, F16, 39) (dual of [642, 560, 40]-code), using
- trace code [i] based on linear OA(25641, 321, F256, 39) (dual of [321, 280, 40]-code), using
- extended algebraic-geometric code AGe(F,281P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25641, 321, F256, 39) (dual of [321, 280, 40]-code), using
- 46 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0) [i] based on linear OA(1682, 642, F16, 39) (dual of [642, 560, 40]-code), using
(50, 89, 199562)-Net in Base 16 — Upper bound on s
There is no (50, 89, 199563)-net in base 16, because
- 1 times m-reduction [i] would yield (50, 88, 199563)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 9174 538969 594350 039007 840019 202322 942742 717069 117322 855043 508342 006012 364026 139134 080876 492129 278076 421056 > 1688 [i]