Best Known (16, 16+10, s)-Nets in Base 4
(16, 16+10, 76)-Net over F4 — Constructive and digital
Digital (16, 26, 76)-net over F4, using
- trace code for nets [i] based on digital (3, 13, 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
(16, 16+10, 91)-Net over F4 — Digital
Digital (16, 26, 91)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(426, 91, F4, 10) (dual of [91, 65, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(426, 94, F4, 10) (dual of [94, 68, 11]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(425, 92, F4, 10) (dual of [92, 67, 11]-code), using
- a “GraX†code from Grassl’s database [i]
- linear OA(425, 93, F4, 9) (dual of [93, 68, 10]-code), using Gilbert–Varšamov bound and bm = 425 > Vbs−1(k−1) = 630 395039 240035 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(425, 92, F4, 10) (dual of [92, 67, 11]-code), using
- construction X with Varšamov bound [i] based on
- discarding factors / shortening the dual code based on linear OA(426, 94, F4, 10) (dual of [94, 68, 11]-code), using
(16, 16+10, 1169)-Net in Base 4 — Upper bound on s
There is no (16, 26, 1170)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 4509 623724 642388 > 426 [i]