Best Known (49, 87, s)-Nets in Base 27
(49, 87, 228)-Net over F27 — Constructive and digital
Digital (49, 87, 228)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 18, 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, 25, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 44, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 18, 76)-net over F27, using
(49, 87, 370)-Net in Base 27 — Constructive
(49, 87, 370)-net in base 27, using
- t-expansion [i] based on (43, 87, 370)-net in base 27, using
- 21 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
- 21 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(49, 87, 1326)-Net over F27 — Digital
Digital (49, 87, 1326)-net over F27, using
(49, 87, 1092389)-Net in Base 27 — Upper bound on s
There is no (49, 87, 1092390)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 33779 179343 867559 544257 442954 661055 532524 553671 309489 117270 912998 748776 706283 786446 553406 211083 207910 891229 926721 378326 147793 > 2787 [i]