Best Known (42, 42+46, s)-Nets in Base 27
(42, 42+46, 182)-Net over F27 — Constructive and digital
Digital (42, 88, 182)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 32, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (10, 56, 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 (9, 32, 88)-net over F27, using
(42, 42+46, 370)-Net in Base 27 — Constructive
(42, 88, 370)-net in base 27, using
- 16 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+46, 430)-Net over F27 — Digital
Digital (42, 88, 430)-net over F27, using
(42, 42+46, 108631)-Net in Base 27 — Upper bound on s
There is no (42, 88, 108632)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 912040 485529 116178 281715 963860 121279 177239 093580 629833 896760 587752 558701 329938 690763 827853 970361 798686 362347 266931 479648 077665 > 2788 [i]