Best Known (38, 38+40, s)-Nets in Base 27
(38, 38+40, 178)-Net over F27 — Constructive and digital
Digital (38, 78, 178)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (8, 28, 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, 50, 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, 28, 84)-net over F27, using
(38, 38+40, 370)-Net in Base 27 — Constructive
(38, 78, 370)-net in base 27, using
- 10 times m-reduction [i] based on (38, 88, 370)-net in base 27, using
- base change [i] based on digital (16, 66, 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, 66, 370)-net over F81, using
(38, 38+40, 443)-Net over F27 — Digital
Digital (38, 78, 443)-net over F27, using
(38, 38+40, 122071)-Net in Base 27 — Upper bound on s
There is no (38, 78, 122072)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 4429 902757 980495 263201 744671 530897 647535 644766 268443 458107 063283 205161 490761 692689 510156 160057 922243 631675 980481 > 2778 [i]