Best Known (48, 90, s)-Nets in Base 3
(48, 90, 56)-Net over F3 — Constructive and digital
Digital (48, 90, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 45, 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
(48, 90, 63)-Net over F3 — Digital
Digital (48, 90, 63)-net over F3, using
(48, 90, 460)-Net in Base 3 — Upper bound on s
There is no (48, 90, 461)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 8 730528 594830 379695 452252 450683 747651 051627 > 390 [i]