Best Known (55, 55+42, s)-Nets in Base 16
(55, 55+42, 526)-Net over F16 — Constructive and digital
Digital (55, 97, 526)-net over F16, using
- 1 times m-reduction [i] based on digital (55, 98, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 49, 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, 49, 263)-net over F256, using
(55, 55+42, 781)-Net over F16 — Digital
Digital (55, 97, 781)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1697, 781, F16, 42) (dual of [781, 684, 43]-code), using
- 130 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 36 times 0, 1, 46 times 0) [i] based on linear OA(1688, 642, F16, 42) (dual of [642, 554, 43]-code), using
- trace code [i] based on linear OA(25644, 321, F256, 42) (dual of [321, 277, 43]-code), using
- extended algebraic-geometric code AGe(F,278P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25644, 321, F256, 42) (dual of [321, 277, 43]-code), using
- 130 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 36 times 0, 1, 46 times 0) [i] based on linear OA(1688, 642, F16, 42) (dual of [642, 554, 43]-code), using
(55, 55+42, 210991)-Net in Base 16 — Upper bound on s
There is no (55, 97, 210992)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 630 450570 595257 138688 131689 910823 525282 706170 682184 818896 249151 139249 713964 631771 588383 174348 964097 207019 710783 331106 > 1697 [i]