Best Known (51, 51+31, s)-Nets in Base 81
(51, 51+31, 812)-Net over F81 — Constructive and digital
Digital (51, 82, 812)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (0, 15, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- digital (36, 67, 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
- digital (0, 15, 82)-net over F81, using
(51, 51+31, 24802)-Net over F81 — Digital
Digital (51, 82, 24802)-net over F81, using
(51, 51+31, large)-Net in Base 81 — Upper bound on s
There is no (51, 82, large)-net in base 81, because
- 29 times m-reduction [i] would yield (51, 53, large)-net in base 81, but