Best Known (45, 45+34, s)-Nets in Base 16
(45, 45+34, 524)-Net over F16 — Constructive and digital
Digital (45, 79, 524)-net over F16, using
- 1 times m-reduction [i] based on digital (45, 80, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 40, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 40, 262)-net over F256, using
(45, 45+34, 701)-Net over F16 — Digital
Digital (45, 79, 701)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1679, 701, F16, 34) (dual of [701, 622, 35]-code), using
- 52 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 14 times 0, 1, 28 times 0) [i] based on linear OA(1672, 642, F16, 34) (dual of [642, 570, 35]-code), using
- trace code [i] based on linear OA(25636, 321, F256, 34) (dual of [321, 285, 35]-code), using
- extended algebraic-geometric code AGe(F,286P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25636, 321, F256, 34) (dual of [321, 285, 35]-code), using
- 52 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 14 times 0, 1, 28 times 0) [i] based on linear OA(1672, 642, F16, 34) (dual of [642, 570, 35]-code), using
(45, 45+34, 188559)-Net in Base 16 — Upper bound on s
There is no (45, 79, 188560)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 133500 585415 530841 449428 515818 722130 242541 189182 437130 374548 497968 676402 006928 878829 222841 415176 > 1679 [i]