Best Known (38, 64, s)-Nets in Base 16
(38, 64, 526)-Net over F16 — Constructive and digital
Digital (38, 64, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 32, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(38, 64, 835)-Net over F16 — Digital
Digital (38, 64, 835)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1664, 835, F16, 26) (dual of [835, 771, 27]-code), using
- 185 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 4 times 0, 1, 13 times 0, 1, 29 times 0, 1, 54 times 0, 1, 78 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
- 185 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 4 times 0, 1, 13 times 0, 1, 29 times 0, 1, 54 times 0, 1, 78 times 0) [i] based on linear OA(1656, 642, F16, 26) (dual of [642, 586, 27]-code), using
(38, 64, 320096)-Net in Base 16 — Upper bound on s
There is no (38, 64, 320097)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 115794 521711 059390 553322 333312 441485 288334 114771 393845 288337 200438 427662 518816 > 1664 [i]