Best Known (8, 8+11, s)-Nets in Base 8
(8, 8+11, 35)-Net over F8 — Constructive and digital
Digital (8, 19, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
(8, 8+11, 38)-Net in Base 8 — Constructive
(8, 19, 38)-net in base 8, using
- 1 times m-reduction [i] based on (8, 20, 38)-net in base 8, using
- base change [i] based on digital (3, 15, 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
- base change [i] based on digital (3, 15, 38)-net over F16, using
(8, 8+11, 660)-Net in Base 8 — Upper bound on s
There is no (8, 19, 661)-net in base 8, because
- 1 times m-reduction [i] would yield (8, 18, 661)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 18038 558092 380792 > 818 [i]