Best Known (37, 37+47, s)-Nets in Base 27
(37, 37+47, 164)-Net over F27 — Constructive and digital
Digital (37, 84, 164)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 30, 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 (7, 54, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (7, 30, 82)-net over F27, using
(37, 37+47, 279)-Net over F27 — Digital
Digital (37, 84, 279)-net over F27, using
(37, 37+47, 370)-Net in Base 27 — Constructive
(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
(37, 37+47, 53056)-Net in Base 27 — Upper bound on s
There is no (37, 84, 53057)-net in base 27, because
- 1 times m-reduction [i] would yield (37, 83, 53057)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 63564 046677 252530 776309 439326 183806 039232 467339 217359 294693 949371 927727 788174 918865 138142 224486 293077 742210 951407 580915 > 2783 [i]