Best Known (52−41, 52, s)-Nets in Base 27
(52−41, 52, 96)-Net over F27 — Constructive and digital
Digital (11, 52, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
(52−41, 52, 100)-Net over F27 — Digital
Digital (11, 52, 100)-net over F27, using
- net from sequence [i] based on digital (11, 99)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 100, using
(52−41, 52, 1416)-Net in Base 27 — Upper bound on s
There is no (11, 52, 1417)-net in base 27, because
- 1 times m-reduction [i] would yield (11, 51, 1417)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 10 077604 464487 212458 997979 570951 670612 458420 397760 495191 049129 128712 734577 > 2751 [i]