Best Known (60, 60+43, s)-Nets in Base 16
(60, 60+43, 530)-Net over F16 — Constructive and digital
Digital (60, 103, 530)-net over F16, using
- 1 times m-reduction [i] based on digital (60, 104, 530)-net over F16, using
- trace code for nets [i] based on digital (8, 52, 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, 52, 265)-net over F256, using
(60, 60+43, 1035)-Net over F16 — Digital
Digital (60, 103, 1035)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16103, 1035, F16, 43) (dual of [1035, 932, 44]-code), using
- 8 step Varšamov–Edel lengthening with (ri) = (1, 7 times 0) [i] based on linear OA(16102, 1026, F16, 43) (dual of [1026, 924, 44]-code), using
- trace code [i] based on linear OA(25651, 513, F256, 43) (dual of [513, 462, 44]-code), using
- extended algebraic-geometric code AGe(F,469P) [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,469P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25651, 513, F256, 43) (dual of [513, 462, 44]-code), using
- 8 step Varšamov–Edel lengthening with (ri) = (1, 7 times 0) [i] based on linear OA(16102, 1026, F16, 43) (dual of [1026, 924, 44]-code), using
(60, 60+43, 408293)-Net in Base 16 — Upper bound on s
There is no (60, 103, 408294)-net in base 16, because
- 1 times m-reduction [i] would yield (60, 102, 408294)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 661 089293 860843 411352 384951 246963 591614 861914 164752 711831 226107 614007 119131 121188 523665 597813 294485 801235 807746 525102 249486 > 16102 [i]