Best Known (61, 61+44, s)-Nets in Base 16
(61, 61+44, 530)-Net over F16 — Constructive and digital
Digital (61, 105, 530)-net over F16, using
- 1 times m-reduction [i] based on digital (61, 106, 530)-net over F16, using
- trace code for nets [i] based on digital (8, 53, 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, 53, 265)-net over F256, using
(61, 61+44, 1033)-Net over F16 — Digital
Digital (61, 105, 1033)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16105, 1033, F16, 44) (dual of [1033, 928, 45]-code), using
- 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) [i] based on linear OA(16104, 1026, F16, 44) (dual of [1026, 922, 45]-code), using
- trace code [i] based on linear OA(25652, 513, F256, 44) (dual of [513, 461, 45]-code), using
- extended algebraic-geometric code AGe(F,468P) [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,468P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25652, 513, F256, 44) (dual of [513, 461, 45]-code), using
- 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) [i] based on linear OA(16104, 1026, F16, 44) (dual of [1026, 922, 45]-code), using
(61, 61+44, 337040)-Net in Base 16 — Upper bound on s
There is no (61, 105, 337041)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 707699 675845 986840 745363 852467 696880 404517 912451 413676 650605 018120 140648 364432 399360 096233 684854 934351 649740 710543 831941 640256 > 16105 [i]