Best Known (103−47, 103, s)-Nets in Base 27
(103−47, 103, 228)-Net over F27 — Constructive and digital
Digital (56, 103, 228)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 21, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (6, 29, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 53, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 21, 76)-net over F27, using
(103−47, 103, 370)-Net in Base 27 — Constructive
(56, 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
(103−47, 103, 1133)-Net over F27 — Digital
Digital (56, 103, 1133)-net over F27, using
(103−47, 103, 807725)-Net in Base 27 — Upper bound on s
There is no (56, 103, 807726)-net in base 27, because
- 1 times m-reduction [i] would yield (56, 102, 807726)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 99 795965 964636 450931 182113 748373 970324 688090 120433 357035 871854 864125 561073 819077 251963 314482 921130 976612 600548 899659 785268 234022 838580 056237 728553 > 27102 [i]