Best Known (80−34, 80, s)-Nets in Base 16
(80−34, 80, 526)-Net over F16 — Constructive and digital
Digital (46, 80, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 40, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(80−34, 80, 749)-Net over F16 — Digital
Digital (46, 80, 749)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1680, 749, F16, 34) (dual of [749, 669, 35]-code), using
- 99 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 14 times 0, 1, 28 times 0, 1, 46 times 0) [i] based on linear OA(1672, 642, F16, 34) (dual of [642, 570, 35]-code), using
- trace code [i] based on linear OA(25636, 321, F256, 34) (dual of [321, 285, 35]-code), using
- extended algebraic-geometric code AGe(F,286P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25636, 321, F256, 34) (dual of [321, 285, 35]-code), using
- 99 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 14 times 0, 1, 28 times 0, 1, 46 times 0) [i] based on linear OA(1672, 642, F16, 34) (dual of [642, 570, 35]-code), using
(80−34, 80, 221964)-Net in Base 16 — Upper bound on s
There is no (46, 80, 221965)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 136107 765917 643962 294292 276527 732875 825154 088854 712153 209148 259584 764559 160374 874025 490687 920576 > 1680 [i]