Best Known (39−14, 39, s)-Nets in Base 4
(39−14, 39, 98)-Net over F4 — Constructive and digital
Digital (25, 39, 98)-net over F4, using
- 1 times m-reduction [i] based on digital (25, 40, 98)-net over F4, using
- trace code for nets [i] based on digital (5, 20, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- trace code for nets [i] based on digital (5, 20, 49)-net over F16, using
(39−14, 39, 128)-Net over F4 — Digital
Digital (25, 39, 128)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(439, 128, F4, 14) (dual of [128, 89, 15]-code), using
- a “Gra†code from Grassl’s database [i]
(39−14, 39, 2542)-Net in Base 4 — Upper bound on s
There is no (25, 39, 2543)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 302835 365337 274908 251884 > 439 [i]