Best Known (67, 116, s)-Nets in Base 16
(67, 116, 532)-Net over F16 — Constructive and digital
Digital (67, 116, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 58, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(67, 116, 1049)-Net over F16 — Digital
Digital (67, 116, 1049)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16116, 1049, F16, 49) (dual of [1049, 933, 50]-code), using
- 21 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 18 times 0) [i] based on linear OA(16114, 1026, F16, 49) (dual of [1026, 912, 50]-code), using
- trace code [i] based on linear OA(25657, 513, F256, 49) (dual of [513, 456, 50]-code), using
- extended algebraic-geometric code AGe(F,463P) [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,463P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25657, 513, F256, 49) (dual of [513, 456, 50]-code), using
- 21 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 18 times 0) [i] based on linear OA(16114, 1026, F16, 49) (dual of [1026, 912, 50]-code), using
(67, 116, 384590)-Net in Base 16 — Upper bound on s
There is no (67, 116, 384591)-net in base 16, because
- 1 times m-reduction [i] would yield (67, 115, 384591)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 2 977271 056909 546292 948897 971582 795240 748881 025363 639738 295885 027291 278492 257938 075342 562855 247065 472724 692658 261595 369883 711475 818137 106236 > 16115 [i]