Best Known (50, 50+38, s)-Nets in Base 16
(50, 50+38, 526)-Net over F16 — Constructive and digital
Digital (50, 88, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 44, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(50, 50+38, 737)-Net over F16 — Digital
Digital (50, 88, 737)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1688, 737, F16, 38) (dual of [737, 649, 39]-code), using
- 87 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 25 times 0, 1, 39 times 0) [i] based on linear OA(1680, 642, F16, 38) (dual of [642, 562, 39]-code), using
- trace code [i] based on linear OA(25640, 321, F256, 38) (dual of [321, 281, 39]-code), using
- extended algebraic-geometric code AGe(F,282P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25640, 321, F256, 38) (dual of [321, 281, 39]-code), using
- 87 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 25 times 0, 1, 39 times 0) [i] based on linear OA(1680, 642, F16, 38) (dual of [642, 562, 39]-code), using
(50, 50+38, 199562)-Net in Base 16 — Upper bound on s
There is no (50, 88, 199563)-net in base 16, because
- 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]