Best Known (25−9, 25, s)-Nets in Base 5
(25−9, 25, 104)-Net over F5 — Constructive and digital
Digital (16, 25, 104)-net over F5, using
- 1 times m-reduction [i] based on digital (16, 26, 104)-net over F5, using
- trace code for nets [i] based on digital (3, 13, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- trace code for nets [i] based on digital (3, 13, 52)-net over F25, using
(25−9, 25, 159)-Net over F5 — Digital
Digital (16, 25, 159)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(525, 159, F5, 9) (dual of [159, 134, 10]-code), using
- 29 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 14 times 0) [i] based on linear OA(520, 125, F5, 9) (dual of [125, 105, 10]-code), using
- a “GraX†code from Grassl’s database [i]
- 29 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 14 times 0) [i] based on linear OA(520, 125, F5, 9) (dual of [125, 105, 10]-code), using
(25−9, 25, 8643)-Net in Base 5 — Upper bound on s
There is no (16, 25, 8644)-net in base 5, because
- 1 times m-reduction [i] would yield (16, 24, 8644)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 59619 736020 433665 > 524 [i]