Best Known (62, 106, s)-Nets in Base 16
(62, 106, 532)-Net over F16 — Constructive and digital
Digital (62, 106, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 53, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
(62, 106, 1072)-Net over F16 — Digital
Digital (62, 106, 1072)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16106, 1072, F16, 44) (dual of [1072, 966, 45]-code), using
- 44 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 37 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
- 44 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 37 times 0) [i] based on linear OA(16104, 1026, F16, 44) (dual of [1026, 922, 45]-code), using
(62, 106, 382311)-Net in Base 16 — Upper bound on s
There is no (62, 106, 382312)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 43 324605 743601 189725 214201 905748 568688 985080 211491 736464 949268 347832 730771 703379 834011 112998 760542 270113 512372 231038 446046 828886 > 16106 [i]