Best Known (107−43, 107, s)-Nets in Base 27
(107−43, 107, 276)-Net over F27 — Constructive and digital
Digital (64, 107, 276)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (9, 23, 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, 31, 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 (10, 53, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27 (see above)
- digital (9, 23, 88)-net over F27, using
(107−43, 107, 730)-Net in Base 27 — Constructive
(64, 107, 730)-net in base 27, using
- t-expansion [i] based on (63, 107, 730)-net in base 27, using
- 1 times m-reduction [i] based on (63, 108, 730)-net in base 27, using
- base change [i] based on digital (36, 81, 730)-net over F81, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- base change [i] based on digital (36, 81, 730)-net over F81, using
- 1 times m-reduction [i] based on (63, 108, 730)-net in base 27, using
(107−43, 107, 2835)-Net over F27 — Digital
Digital (64, 107, 2835)-net over F27, using
(107−43, 107, 5603990)-Net in Base 27 — Upper bound on s
There is no (64, 107, 5603991)-net in base 27, because
- 1 times m-reduction [i] would yield (64, 106, 5603991)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 53 034685 350551 023416 149995 067722 858365 487935 035152 700186 292092 711377 359509 079715 063743 944931 637738 581625 271528 458153 106217 873757 200979 463885 328341 639439 > 27106 [i]