Best Known (95−51, 95, s)-Nets in Base 27
(95−51, 95, 182)-Net over F27 — Constructive and digital
Digital (44, 95, 182)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 34, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (10, 61, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (9, 34, 88)-net over F27, using
(95−51, 95, 370)-Net in Base 27 — Constructive
(44, 95, 370)-net in base 27, using
- t-expansion [i] based on (43, 95, 370)-net in base 27, using
- 13 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
- 13 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(95−51, 95, 389)-Net over F27 — Digital
Digital (44, 95, 389)-net over F27, using
(95−51, 95, 94301)-Net in Base 27 — Upper bound on s
There is no (44, 95, 94302)-net in base 27, because
- 1 times m-reduction [i] would yield (44, 94, 94302)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 353 348110 637517 349135 280219 743355 344926 036344 681391 536791 703785 927912 036027 763281 588266 929314 761971 152104 487272 986732 709963 389826 116829 > 2794 [i]