Best Known (113−47, 113, s)-Nets in Base 16
(113−47, 113, 532)-Net over F16 — Constructive and digital
Digital (66, 113, 532)-net over F16, using
- 1 times m-reduction [i] based on digital (66, 114, 532)-net over F16, using
- trace code for nets [i] based on digital (9, 57, 266)-net over F256, using
- net from sequence [i] based on digital (9, 265)-sequence over F256, using
- trace code for nets [i] based on digital (9, 57, 266)-net over F256, using
(113−47, 113, 1113)-Net over F16 — Digital
Digital (66, 113, 1113)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16113, 1113, F16, 47) (dual of [1113, 1000, 48]-code), using
- 84 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 1, 24 times 0, 1, 55 times 0) [i] based on linear OA(16110, 1026, F16, 47) (dual of [1026, 916, 48]-code), using
- trace code [i] based on linear OA(25655, 513, F256, 47) (dual of [513, 458, 48]-code), using
- extended algebraic-geometric code AGe(F,465P) [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,465P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25655, 513, F256, 47) (dual of [513, 458, 48]-code), using
- 84 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 1, 24 times 0, 1, 55 times 0) [i] based on linear OA(16110, 1026, F16, 47) (dual of [1026, 916, 48]-code), using
(113−47, 113, 459085)-Net in Base 16 — Upper bound on s
There is no (66, 113, 459086)-net in base 16, because
- 1 times m-reduction [i] would yield (66, 112, 459086)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 726 842562 461228 650662 920067 359118 419172 108615 199878 089864 480796 852575 233311 735338 337249 483739 322379 214199 181432 620258 194389 358726 030096 > 16112 [i]