Best Known (104−43, 104, s)-Nets in Base 16
(104−43, 104, 532)-Net over F16 — Constructive and digital
Digital (61, 104, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 52, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(104−43, 104, 1079)-Net over F16 — Digital
Digital (61, 104, 1079)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16104, 1079, F16, 43) (dual of [1079, 975, 44]-code), using
- 51 step Varšamov–Edel lengthening with (ri) = (1, 7 times 0, 1, 42 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
- 51 step Varšamov–Edel lengthening with (ri) = (1, 7 times 0, 1, 42 times 0) [i] based on linear OA(16102, 1026, F16, 43) (dual of [1026, 924, 44]-code), using
(104−43, 104, 465921)-Net in Base 16 — Upper bound on s
There is no (61, 104, 465922)-net in base 16, because
- 1 times m-reduction [i] would yield (61, 103, 465922)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 10577 261509 591021 532256 399940 791495 408685 350719 067014 318481 364619 889130 885859 149388 422517 308107 003183 070600 318344 217895 309056 > 16103 [i]