Best Known (69−29, 69, s)-Nets in Base 16
(69−29, 69, 524)-Net over F16 — Constructive and digital
Digital (40, 69, 524)-net over F16, using
- 1 times m-reduction [i] based on digital (40, 70, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 35, 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, 35, 262)-net over F256, using
(69−29, 69, 724)-Net over F16 — Digital
Digital (40, 69, 724)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1669, 724, F16, 29) (dual of [724, 655, 30]-code), using
- 75 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 8 times 0, 1, 20 times 0, 1, 40 times 0) [i] based on linear OA(1662, 642, F16, 29) (dual of [642, 580, 30]-code), using
- trace code [i] based on linear OA(25631, 321, F256, 29) (dual of [321, 290, 30]-code), using
- extended algebraic-geometric code AGe(F,291P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25631, 321, F256, 29) (dual of [321, 290, 30]-code), using
- 75 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 8 times 0, 1, 20 times 0, 1, 40 times 0) [i] based on linear OA(1662, 642, F16, 29) (dual of [642, 580, 30]-code), using
(69−29, 69, 284405)-Net in Base 16 — Upper bound on s
There is no (40, 69, 284406)-net in base 16, because
- 1 times m-reduction [i] would yield (40, 68, 284406)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 7588 758700 699847 348546 187605 663095 055391 676701 400795 907757 375832 547358 946676 133736 > 1668 [i]