Best Known (51, 103, s)-Nets in Base 27
(51, 103, 192)-Net over F27 — Constructive and digital
Digital (51, 103, 192)-net over F27, using
- 6 times m-reduction [i] based on digital (51, 109, 192)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (11, 40, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- digital (11, 69, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27 (see above)
- digital (11, 40, 96)-net over F27, using
- (u, u+v)-construction [i] based on
(51, 103, 370)-Net in Base 27 — Constructive
(51, 103, 370)-net in base 27, using
- t-expansion [i] based on (43, 103, 370)-net in base 27, using
- 5 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 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, 81, 370)-net over F81, using
- 5 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(51, 103, 601)-Net over F27 — Digital
Digital (51, 103, 601)-net over F27, using
(51, 103, 189972)-Net in Base 27 — Upper bound on s
There is no (51, 103, 189973)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2694 506911 630941 720401 961485 414708 036170 864494 598937 731552 392101 156531 308743 842606 525861 446542 603125 112383 038657 291497 077881 506051 268454 145084 787425 > 27103 [i]