Best Known (80−28, 80, s)-Nets in Base 81
(80−28, 80, 846)-Net over F81 — Constructive and digital
Digital (52, 80, 846)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 16, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- digital (36, 64, 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 (2, 16, 116)-net over F81, using
(80−28, 80, 61685)-Net over F81 — Digital
Digital (52, 80, 61685)-net over F81, using
(80−28, 80, large)-Net in Base 81 — Upper bound on s
There is no (52, 80, large)-net in base 81, because
- 26 times m-reduction [i] would yield (52, 54, large)-net in base 81, but