Best Known (37, 37+44, s)-Nets in Base 27
(37, 37+44, 166)-Net over F27 — Constructive and digital
Digital (37, 81, 166)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 29, 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 (8, 52, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (7, 29, 82)-net over F27, using
(37, 37+44, 321)-Net over F27 — Digital
Digital (37, 81, 321)-net over F27, using
(37, 37+44, 370)-Net in Base 27 — Constructive
(37, 81, 370)-net in base 27, using
- 3 times m-reduction [i] based on (37, 84, 370)-net in base 27, using
- base change [i] based on digital (16, 63, 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, 63, 370)-net over F81, using
(37, 37+44, 64837)-Net in Base 27 — Upper bound on s
There is no (37, 81, 64838)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 87 210792 406418 545972 045721 601770 135335 863732 313377 894612 819242 439193 546615 869514 333426 370851 287133 251112 092744 125877 > 2781 [i]