Best Known (72−44, 72, s)-Nets in Base 32
(72−44, 72, 128)-Net over F32 — Constructive and digital
Digital (28, 72, 128)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 25, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (3, 47, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32 (see above)
- digital (3, 25, 64)-net over F32, using
(72−44, 72, 257)-Net over F32 — Digital
Digital (28, 72, 257)-net over F32, using
- net from sequence [i] based on digital (28, 256)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 28 and N(F) ≥ 257, using
(72−44, 72, 258)-Net in Base 32 — Constructive
(28, 72, 258)-net in base 32, using
- base change [i] based on digital (1, 45, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
(72−44, 72, 289)-Net in Base 32
(28, 72, 289)-net in base 32, using
- base change [i] based on digital (1, 45, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
(72−44, 72, 24617)-Net in Base 32 — Upper bound on s
There is no (28, 72, 24618)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 350177 732704 718283 372557 277411 393246 680997 904726 983853 605222 996930 336396 242229 920342 695616 705560 464383 202936 > 3272 [i]