Best Known (58−24, 58, s)-Nets in Base 16
(58−24, 58, 524)-Net over F16 — Constructive and digital
Digital (34, 58, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 29, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
(58−24, 58, 718)-Net over F16 — Digital
Digital (34, 58, 718)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1658, 718, F16, 24) (dual of [718, 660, 25]-code), using
- 70 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 6 times 0, 1, 19 times 0, 1, 39 times 0) [i] based on linear OA(1652, 642, F16, 24) (dual of [642, 590, 25]-code), using
- trace code [i] based on linear OA(25626, 321, F256, 24) (dual of [321, 295, 25]-code), using
- extended algebraic-geometric code AGe(F,296P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25626, 321, F256, 24) (dual of [321, 295, 25]-code), using
- 70 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 6 times 0, 1, 19 times 0, 1, 39 times 0) [i] based on linear OA(1652, 642, F16, 24) (dual of [642, 590, 25]-code), using
(58−24, 58, 232901)-Net in Base 16 — Upper bound on s
There is no (34, 58, 232902)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 6902 044091 117905 932426 559253 346985 805693 886433 006273 502541 621127 352536 > 1658 [i]