Best Known (42, 42+42, s)-Nets in Base 27
(42, 42+42, 190)-Net over F27 — Constructive and digital
Digital (42, 84, 190)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (10, 31, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (11, 53, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- digital (10, 31, 94)-net over F27, using
(42, 42+42, 370)-Net in Base 27 — Constructive
(42, 84, 370)-net in base 27, using
- 20 times m-reduction [i] based on (42, 104, 370)-net in base 27, using
- base change [i] based on digital (16, 78, 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, 78, 370)-net over F81, using
(42, 42+42, 548)-Net over F27 — Digital
Digital (42, 84, 548)-net over F27, using
(42, 42+42, 177397)-Net in Base 27 — Upper bound on s
There is no (42, 84, 177398)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 716228 494009 902756 998546 370989 178177 272406 429239 728985 335380 555339 507971 319173 547805 989418 723235 121587 673803 979040 864949 > 2784 [i]