Best Known (47, 47+41, s)-Nets in Base 3
(47, 47+41, 56)-Net over F3 — Constructive and digital
Digital (47, 88, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 44, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
(47, 47+41, 62)-Net over F3 — Digital
Digital (47, 88, 62)-net over F3, using
(47, 47+41, 474)-Net in Base 3 — Upper bound on s
There is no (47, 88, 475)-net in base 3, because
- 1 times m-reduction [i] would yield (47, 87, 475)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 325283 654973 463759 899651 547180 044892 120761 > 387 [i]