Best Known (91−37, 91, s)-Nets in Base 16
(91−37, 91, 530)-Net over F16 — Constructive and digital
Digital (54, 91, 530)-net over F16, using
- 1 times m-reduction [i] based on digital (54, 92, 530)-net over F16, using
- trace code for nets [i] based on digital (8, 46, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
- trace code for nets [i] based on digital (8, 46, 265)-net over F256, using
(91−37, 91, 1075)-Net over F16 — Digital
Digital (54, 91, 1075)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1691, 1075, F16, 37) (dual of [1075, 984, 38]-code), using
- 48 step Varšamov–Edel lengthening with (ri) = (1, 47 times 0) [i] based on linear OA(1690, 1026, F16, 37) (dual of [1026, 936, 38]-code), using
- trace code [i] based on linear OA(25645, 513, F256, 37) (dual of [513, 468, 38]-code), using
- extended algebraic-geometric code AGe(F,475P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- extended algebraic-geometric code AGe(F,475P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25645, 513, F256, 37) (dual of [513, 468, 38]-code), using
- 48 step Varšamov–Edel lengthening with (ri) = (1, 47 times 0) [i] based on linear OA(1690, 1026, F16, 37) (dual of [1026, 936, 38]-code), using
(91−37, 91, 527996)-Net in Base 16 — Upper bound on s
There is no (54, 91, 527997)-net in base 16, because
- 1 times m-reduction [i] would yield (54, 90, 527997)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 2 348612 910201 551332 942151 548374 753280 335533 327191 449230 554507 954751 379657 205946 174273 689958 029050 036697 158466 > 1690 [i]