Best Known (71−30, 71, s)-Nets in Base 32
(71−30, 71, 240)-Net over F32 — Constructive and digital
Digital (41, 71, 240)-net over F32, using
- 8 times m-reduction [i] based on digital (41, 79, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 30, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (11, 49, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 30, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(71−30, 71, 513)-Net in Base 32 — Constructive
(41, 71, 513)-net in base 32, using
- 7 times m-reduction [i] based on (41, 78, 513)-net in base 32, using
- base change [i] based on digital (28, 65, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 65, 513)-net over F64, using
(71−30, 71, 1837)-Net over F32 — Digital
Digital (41, 71, 1837)-net over F32, using
(71−30, 71, 2759181)-Net in Base 32 — Upper bound on s
There is no (41, 71, 2759182)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 73391 994179 864890 197259 101682 434207 368456 395586 259515 910598 381004 554748 581048 229534 807245 559549 678027 464960 > 3271 [i]