Best Known (8, 8+17, s)-Nets in Base 27
(8, 8+17, 84)-Net over F27 — Constructive and digital
Digital (8, 25, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
(8, 8+17, 92)-Net over F27 — Digital
Digital (8, 25, 92)-net over F27, using
- net from sequence [i] based on digital (8, 91)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 92, using
(8, 8+17, 100)-Net in Base 27 — Constructive
(8, 25, 100)-net in base 27, using
- 3 times m-reduction [i] based on (8, 28, 100)-net in base 27, using
- base change [i] based on digital (1, 21, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- base change [i] based on digital (1, 21, 100)-net over F81, using
(8, 8+17, 2845)-Net in Base 27 — Upper bound on s
There is no (8, 25, 2846)-net in base 27, because
- 1 times m-reduction [i] would yield (8, 24, 2846)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 22531 447563 969143 440827 965822 003793 > 2724 [i]