Best Known (42, 95, s)-Nets in Base 27
(42, 95, 170)-Net over F27 — Constructive and digital
Digital (42, 95, 170)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 33, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (9, 62, 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 (7, 33, 82)-net over F27, using
(42, 95, 312)-Net over F27 — Digital
Digital (42, 95, 312)-net over F27, using
(42, 95, 370)-Net in Base 27 — Constructive
(42, 95, 370)-net in base 27, using
- 9 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, 95, 60695)-Net in Base 27 — Upper bound on s
There is no (42, 95, 60696)-net in base 27, because
- 1 times m-reduction [i] would yield (42, 94, 60696)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 353 476830 472710 508588 342776 943528 203600 798755 129515 163939 118781 674169 861864 279593 434958 393076 460563 874639 666481 870421 670450 756950 445713 > 2794 [i]