Best Known (45, 45+32, s)-Nets in Base 81
(45, 45+32, 730)-Net over F81 — Constructive and digital
Digital (45, 77, 730)-net over F81, using
- t-expansion [i] based on digital (36, 77, 730)-net over F81, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
(45, 45+32, 8554)-Net over F81 — Digital
Digital (45, 77, 8554)-net over F81, using
(45, 45+32, large)-Net in Base 81 — Upper bound on s
There is no (45, 77, large)-net in base 81, because
- 30 times m-reduction [i] would yield (45, 47, large)-net in base 81, but