Best Known (87−38, 87, s)-Nets in Base 16
(87−38, 87, 524)-Net over F16 — Constructive and digital
Digital (49, 87, 524)-net over F16, using
- 1 times m-reduction [i] based on digital (49, 88, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 44, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 44, 262)-net over F256, using
(87−38, 87, 696)-Net over F16 — Digital
Digital (49, 87, 696)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1687, 696, F16, 38) (dual of [696, 609, 39]-code), using
- 47 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 25 times 0) [i] based on linear OA(1680, 642, F16, 38) (dual of [642, 562, 39]-code), using
- trace code [i] based on linear OA(25640, 321, F256, 38) (dual of [321, 281, 39]-code), using
- extended algebraic-geometric code AGe(F,282P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25640, 321, F256, 38) (dual of [321, 281, 39]-code), using
- 47 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 25 times 0) [i] based on linear OA(1680, 642, F16, 38) (dual of [642, 562, 39]-code), using
(87−38, 87, 172464)-Net in Base 16 — Upper bound on s
There is no (49, 87, 172465)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 573 388488 904646 250554 707326 283893 604818 256838 618537 660384 986641 158100 704879 944083 334676 202675 815237 015776 > 1687 [i]