Best Known (40, 89, s)-Nets in Base 27
(40, 89, 170)-Net over F27 — Constructive and digital
Digital (40, 89, 170)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 31, 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 (9, 58, 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 (7, 31, 82)-net over F27, using
(40, 89, 319)-Net over F27 — Digital
Digital (40, 89, 319)-net over F27, using
(40, 89, 370)-Net in Base 27 — Constructive
(40, 89, 370)-net in base 27, using
- 7 times m-reduction [i] based on (40, 96, 370)-net in base 27, using
- base change [i] based on digital (16, 72, 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, 72, 370)-net over F81, using
(40, 89, 66779)-Net in Base 27 — Upper bound on s
There is no (40, 89, 66780)-net in base 27, because
- 1 times m-reduction [i] would yield (40, 88, 66780)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 912236 351944 156118 537981 346516 515909 511062 519278 805642 412262 063396 288692 042007 107829 630115 326507 719775 925162 891895 994930 026561 > 2788 [i]