Best Known (41, 41+46, s)-Nets in Base 27
(41, 41+46, 178)-Net over F27 — Constructive and digital
Digital (41, 87, 178)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (8, 31, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (10, 56, 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 (8, 31, 84)-net over F27, using
(41, 41+46, 370)-Net in Base 27 — Constructive
(41, 87, 370)-net in base 27, using
- 13 times m-reduction [i] based on (41, 100, 370)-net in base 27, using
- base change [i] based on digital (16, 75, 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, 75, 370)-net over F81, using
(41, 41+46, 398)-Net over F27 — Digital
Digital (41, 87, 398)-net over F27, using
(41, 41+46, 94127)-Net in Base 27 — Upper bound on s
There is no (41, 87, 94128)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 33782 108859 827299 452760 764417 941675 060818 679585 902641 154426 048505 268899 935019 815042 530789 715527 875795 616982 888115 304819 399873 > 2787 [i]