Best Known (103−48, 103, s)-Nets in Base 27
(103−48, 103, 210)-Net over F27 — Constructive and digital
Digital (55, 103, 210)-net over F27, using
- 1 times m-reduction [i] based on digital (55, 104, 210)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 20, 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, 28, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (7, 56, 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, 20, 64)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(103−48, 103, 370)-Net in Base 27 — Constructive
(55, 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
(103−48, 103, 992)-Net over F27 — Digital
Digital (55, 103, 992)-net over F27, using
(103−48, 103, 523980)-Net in Base 27 — Upper bound on s
There is no (55, 103, 523981)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2694 478624 878138 615586 843289 146116 313257 708220 086416 331631 989542 366686 934078 803695 606270 211397 936796 258942 916765 204877 540291 056188 333299 348272 862433 > 27103 [i]