Best Known (8, 8+12, s)-Nets in Base 27
(8, 8+12, 84)-Net over F27 — Constructive and digital
Digital (8, 20, 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+12, 92)-Net over F27 — Digital
Digital (8, 20, 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+12, 116)-Net in Base 27 — Constructive
(8, 20, 116)-net in base 27, using
- 4 times m-reduction [i] based on (8, 24, 116)-net in base 27, using
- base change [i] based on digital (2, 18, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 18, 116)-net over F81, using
(8, 8+12, 136)-Net in Base 27
(8, 20, 136)-net in base 27, using
- base change [i] based on digital (3, 15, 136)-net over F81, using
- net from sequence [i] based on digital (3, 135)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 3 and N(F) ≥ 136, using
- net from sequence [i] based on digital (3, 135)-sequence over F81, using
(8, 8+12, 6796)-Net in Base 27 — Upper bound on s
There is no (8, 20, 6797)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 42408 975409 675019 055758 486913 > 2720 [i]