Best Known (45, 78, s)-Nets in Base 16
(45, 78, 526)-Net over F16 — Constructive and digital
Digital (45, 78, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 39, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(45, 78, 753)-Net over F16 — Digital
Digital (45, 78, 753)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1678, 753, F16, 33) (dual of [753, 675, 34]-code), using
- 103 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 14 times 0, 1, 30 times 0, 1, 48 times 0) [i] based on linear OA(1670, 642, F16, 33) (dual of [642, 572, 34]-code), using
- trace code [i] based on linear OA(25635, 321, F256, 33) (dual of [321, 286, 34]-code), using
- extended algebraic-geometric code AGe(F,287P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25635, 321, F256, 33) (dual of [321, 286, 34]-code), using
- 103 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 14 times 0, 1, 30 times 0, 1, 48 times 0) [i] based on linear OA(1670, 642, F16, 33) (dual of [642, 572, 34]-code), using
(45, 78, 282658)-Net in Base 16 — Upper bound on s
There is no (45, 78, 282659)-net in base 16, because
- 1 times m-reduction [i] would yield (45, 77, 282659)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 521 502307 550496 682538 290034 615599 761865 742328 569601 106724 036328 706687 809806 029363 787707 731286 > 1677 [i]