Best Known (60−31, 60, s)-Nets in Base 9
(60−31, 60, 80)-Net over F9 — Constructive and digital
Digital (29, 60, 80)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (1, 16, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- digital (13, 44, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (1, 16, 16)-net over F9, using
(60−31, 60, 88)-Net in Base 9 — Constructive
(29, 60, 88)-net in base 9, using
- base change [i] based on digital (9, 40, 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
(60−31, 60, 116)-Net over F9 — Digital
Digital (29, 60, 116)-net over F9, using
(60−31, 60, 4541)-Net in Base 9 — Upper bound on s
There is no (29, 60, 4542)-net in base 9, because
- 1 times m-reduction [i] would yield (29, 59, 4542)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 200 108815 360337 258479 252458 674781 455956 457551 972621 222737 > 959 [i]