Best Known (72−53, 72, s)-Nets in Base 32
(72−53, 72, 120)-Net over F32 — Constructive and digital
Digital (19, 72, 120)-net over F32, using
- t-expansion [i] based on digital (11, 72, 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
(72−53, 72, 172)-Net over F32 — Digital
Digital (19, 72, 172)-net over F32, using
- net from sequence [i] based on digital (19, 171)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 19 and N(F) ≥ 172, using
(72−53, 72, 177)-Net in Base 32 — Constructive
(19, 72, 177)-net in base 32, using
- base change [i] based on digital (7, 60, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
(72−53, 72, 4373)-Net in Base 32 — Upper bound on s
There is no (19, 72, 4374)-net in base 32, because
- 1 times m-reduction [i] would yield (19, 71, 4374)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 73619 428284 833070 435448 882276 749932 190864 763382 441630 322684 015302 003528 558986 477880 841597 201090 965021 408320 > 3271 [i]