Best Known (34, 34+36, s)-Nets in Base 27
(34, 34+36, 170)-Net over F27 — Constructive and digital
Digital (34, 70, 170)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 25, 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, 45, 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, 25, 82)-net over F27, using
(34, 34+36, 370)-Net in Base 27 — Constructive
(34, 70, 370)-net in base 27, using
- 2 times m-reduction [i] based on (34, 72, 370)-net in base 27, using
- base change [i] based on digital (16, 54, 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, 54, 370)-net over F81, using
(34, 34+36, 403)-Net over F27 — Digital
Digital (34, 70, 403)-net over F27, using
(34, 34+36, 107037)-Net in Base 27 — Upper bound on s
There is no (34, 70, 107038)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 15686 797325 228896 698488 512515 484852 396842 283444 670322 049718 934176 395944 854477 627262 690281 191419 304989 > 2770 [i]