Best Known (54, 54+41, s)-Nets in Base 16
(54, 54+41, 526)-Net over F16 — Constructive and digital
Digital (54, 95, 526)-net over F16, using
- 1 times m-reduction [i] based on digital (54, 96, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 48, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 48, 263)-net over F256, using
(54, 54+41, 782)-Net over F16 — Digital
Digital (54, 95, 782)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1695, 782, F16, 41) (dual of [782, 687, 42]-code), using
- 131 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 37 times 0, 1, 46 times 0) [i] based on linear OA(1686, 642, F16, 41) (dual of [642, 556, 42]-code), using
- trace code [i] based on linear OA(25643, 321, F256, 41) (dual of [321, 278, 42]-code), using
- extended algebraic-geometric code AGe(F,279P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25643, 321, F256, 41) (dual of [321, 278, 42]-code), using
- 131 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 37 times 0, 1, 46 times 0) [i] based on linear OA(1686, 642, F16, 41) (dual of [642, 556, 42]-code), using
(54, 54+41, 252673)-Net in Base 16 — Upper bound on s
There is no (54, 95, 252674)-net in base 16, because
- 1 times m-reduction [i] would yield (54, 94, 252674)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 153916 106604 722771 521650 124026 505875 891121 927457 153581 761169 641271 360810 913731 362084 106163 829270 794009 703091 936576 > 1694 [i]