Best Known (36, 62, s)-Nets in Base 16
(36, 62, 524)-Net over F16 — Constructive and digital
Digital (36, 62, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 31, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
(36, 62, 699)-Net over F16 — Digital
Digital (36, 62, 699)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1662, 699, F16, 26) (dual of [699, 637, 27]-code), using
- 51 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 4 times 0, 1, 13 times 0, 1, 29 times 0) [i] based on linear OA(1656, 642, F16, 26) (dual of [642, 586, 27]-code), using
- trace code [i] based on linear OA(25628, 321, F256, 26) (dual of [321, 293, 27]-code), using
- extended algebraic-geometric code AGe(F,294P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25628, 321, F256, 26) (dual of [321, 293, 27]-code), using
- 51 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 4 times 0, 1, 13 times 0, 1, 29 times 0) [i] based on linear OA(1656, 642, F16, 26) (dual of [642, 586, 27]-code), using
(36, 62, 208942)-Net in Base 16 — Upper bound on s
There is no (36, 62, 208943)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 452 327850 033595 092447 132960 977612 846134 149093 182348 531616 516491 264930 626186 > 1662 [i]