Best Known (14−8, 14, s)-Nets in Base 8
(14−8, 14, 28)-Net over F8 — Constructive and digital
Digital (6, 14, 28)-net over F8, using
- t-expansion [i] based on digital (5, 14, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
(14−8, 14, 33)-Net in Base 8 — Constructive
(6, 14, 33)-net in base 8, using
- 2 times m-reduction [i] based on (6, 16, 33)-net in base 8, using
- base change [i] based on digital (2, 12, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- base change [i] based on digital (2, 12, 33)-net over F16, using
(14−8, 14, 37)-Net over F8 — Digital
Digital (6, 14, 37)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(814, 37, F8, 8) (dual of [37, 23, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(814, 63, F8, 8) (dual of [63, 49, 9]-code), using
(14−8, 14, 455)-Net in Base 8 — Upper bound on s
There is no (6, 14, 456)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 4 404539 061651 > 814 [i]