Best Known (22−8, 22, s)-Nets in Base 4
(22−8, 22, 76)-Net over F4 — Constructive and digital
Digital (14, 22, 76)-net over F4, using
- trace code for nets [i] based on digital (3, 11, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
(22−8, 22, 124)-Net over F4 — Digital
Digital (14, 22, 124)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(422, 124, F4, 8) (dual of [124, 102, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(422, 133, F4, 8) (dual of [133, 111, 9]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(422, 133, F4, 8) (dual of [133, 111, 9]-code), using
(22−8, 22, 1508)-Net in Base 4 — Upper bound on s
There is no (14, 22, 1509)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 17 631405 878329 > 422 [i]