Best Known (44−18, 44, s)-Nets in Base 16
(44−18, 44, 522)-Net over F16 — Constructive and digital
Digital (26, 44, 522)-net over F16, using
- trace code for nets [i] based on digital (4, 22, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
(44−18, 44, 684)-Net over F16 — Digital
Digital (26, 44, 684)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1644, 684, F16, 18) (dual of [684, 640, 19]-code), using
- 38 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 7 times 0, 1, 27 times 0) [i] based on linear OA(1640, 642, F16, 18) (dual of [642, 602, 19]-code), using
- trace code [i] based on linear OA(25620, 321, F256, 18) (dual of [321, 301, 19]-code), using
- extended algebraic-geometric code AGe(F,302P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25620, 321, F256, 18) (dual of [321, 301, 19]-code), using
- 38 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 7 times 0, 1, 27 times 0) [i] based on linear OA(1640, 642, F16, 18) (dual of [642, 602, 19]-code), using
(44−18, 44, 213039)-Net in Base 16 — Upper bound on s
There is no (26, 44, 213040)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 95784 023137 074269 407790 142944 489498 941841 906246 526151 > 1644 [i]