Best Known (21, 21+44, s)-Nets in Base 27
(21, 21+44, 108)-Net over F27 — Constructive and digital
Digital (21, 65, 108)-net over F27, using
- t-expansion [i] based on digital (18, 65, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
(21, 21+44, 150)-Net in Base 27 — Constructive
(21, 65, 150)-net in base 27, using
- 3 times m-reduction [i] based on (21, 68, 150)-net in base 27, using
- base change [i] based on digital (4, 51, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- base change [i] based on digital (4, 51, 150)-net over F81, using
(21, 21+44, 163)-Net over F27 — Digital
Digital (21, 65, 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
(21, 21+44, 5889)-Net in Base 27 — Upper bound on s
There is no (21, 65, 5890)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1095 375408 613695 877918 339867 553277 355776 301078 209557 610322 128081 968374 687406 921958 081219 508509 > 2765 [i]