Best Known (59, 101, s)-Nets in Base 16
(59, 101, 530)-Net over F16 — Constructive and digital
Digital (59, 101, 530)-net over F16, using
- 1 times m-reduction [i] based on digital (59, 102, 530)-net over F16, using
- trace code for nets [i] based on digital (8, 51, 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, 51, 265)-net over F256, using
(59, 101, 1038)-Net over F16 — Digital
Digital (59, 101, 1038)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16101, 1038, F16, 42) (dual of [1038, 937, 43]-code), using
- 11 step Varšamov–Edel lengthening with (ri) = (1, 10 times 0) [i] based on linear OA(16100, 1026, F16, 42) (dual of [1026, 926, 43]-code), using
- trace code [i] based on linear OA(25650, 513, F256, 42) (dual of [513, 463, 43]-code), using
- extended algebraic-geometric code AGe(F,470P) [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,470P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25650, 513, F256, 42) (dual of [513, 463, 43]-code), using
- 11 step Varšamov–Edel lengthening with (ri) = (1, 10 times 0) [i] based on linear OA(16100, 1026, F16, 42) (dual of [1026, 926, 43]-code), using
(59, 101, 357792)-Net in Base 16 — Upper bound on s
There is no (59, 101, 357793)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 41 317281 651140 317432 428324 837574 222546 433751 606983 117950 662830 621702 607165 171457 347537 619001 941615 631268 551300 221850 603296 > 16101 [i]