Best Known (78−56, 78, s)-Nets in Base 27
(78−56, 78, 112)-Net over F27 — Constructive and digital
Digital (22, 78, 112)-net over F27, using
- net from sequence [i] based on digital (22, 111)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 22 and N(F) ≥ 112, using
(78−56, 78, 116)-Net in Base 27 — Constructive
(22, 78, 116)-net in base 27, using
- 2 times m-reduction [i] based on (22, 80, 116)-net in base 27, using
- base change [i] based on digital (2, 60, 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, 60, 116)-net over F81, using
(78−56, 78, 163)-Net over F27 — Digital
Digital (22, 78, 163)-net over F27, using
- t-expansion [i] based on digital (21, 78, 163)-net over F27, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 21 and N(F) ≥ 163, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
(78−56, 78, 4206)-Net in Base 27 — Upper bound on s
There is no (22, 78, 4207)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 4450 124700 409826 863336 221750 618481 113109 796194 048137 309052 320855 231617 547359 194268 304377 015118 507750 212496 093225 > 2778 [i]