Best Known (37, 64, s)-Nets in Base 27
(37, 64, 210)-Net over F27 — Constructive and digital
Digital (37, 64, 210)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 13, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 17, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (7, 34, 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 (4, 13, 64)-net over F27, using
(37, 64, 370)-Net in Base 27 — Constructive
(37, 64, 370)-net in base 27, using
- 20 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, 64, 1367)-Net over F27 — Digital
Digital (37, 64, 1367)-net over F27, using
(37, 64, 1883824)-Net in Base 27 — Upper bound on s
There is no (37, 64, 1883825)-net in base 27, because
- 1 times m-reduction [i] would yield (37, 63, 1883825)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 499408 320697 213872 131967 966931 717122 878603 421819 542624 615926 290978 829163 904359 400347 593451 > 2763 [i]