Best Known (58, 58+49, s)-Nets in Base 27
(58, 58+49, 228)-Net over F27 — Constructive and digital
Digital (58, 107, 228)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 22, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (6, 30, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 55, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 22, 76)-net over F27, using
(58, 58+49, 370)-Net in Base 27 — Constructive
(58, 107, 370)-net in base 27, using
- t-expansion [i] based on (43, 107, 370)-net in base 27, using
- 1 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- 1 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(58, 58+49, 1142)-Net over F27 — Digital
Digital (58, 107, 1142)-net over F27, using
(58, 58+49, 791114)-Net in Base 27 — Upper bound on s
There is no (58, 107, 791115)-net in base 27, because
- 1 times m-reduction [i] would yield (58, 106, 791115)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 53 035810 833504 340485 121954 844104 912534 553120 842279 404668 184175 982948 696653 019809 680870 464620 733810 408414 517655 720324 299917 284462 723940 716382 371272 727569 > 27106 [i]