Best Known (41, 41+29, s)-Nets in Base 16
(41, 41+29, 526)-Net over F16 — Constructive and digital
Digital (41, 70, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 35, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(41, 41+29, 788)-Net over F16 — Digital
Digital (41, 70, 788)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1670, 788, F16, 29) (dual of [788, 718, 30]-code), using
- 138 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 8 times 0, 1, 20 times 0, 1, 40 times 0, 1, 62 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
- 138 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 8 times 0, 1, 20 times 0, 1, 40 times 0, 1, 62 times 0) [i] based on linear OA(1662, 642, F16, 29) (dual of [642, 580, 30]-code), using
(41, 41+29, 346695)-Net in Base 16 — Upper bound on s
There is no (41, 70, 346696)-net in base 16, because
- 1 times m-reduction [i] would yield (41, 69, 346696)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 121418 053898 842014 837403 803367 584841 537427 174947 791813 379328 964602 940389 411978 658136 > 1669 [i]