Best Known (80−61, 80, s)-Nets in Base 32
(80−61, 80, 120)-Net over F32 — Constructive and digital
Digital (19, 80, 120)-net over F32, using
- t-expansion [i] based on digital (11, 80, 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
(80−61, 80, 128)-Net in Base 32 — Constructive
(19, 80, 128)-net in base 32, using
- 4 times m-reduction [i] based on (19, 84, 128)-net in base 32, using
- base change [i] based on digital (5, 70, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- base change [i] based on digital (5, 70, 128)-net over F64, using
(80−61, 80, 172)-Net over F32 — Digital
Digital (19, 80, 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
(80−61, 80, 3557)-Net in Base 32 — Upper bound on s
There is no (19, 80, 3558)-net in base 32, because
- 1 times m-reduction [i] would yield (19, 79, 3558)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 81251 944699 822053 767146 635297 874965 464130 760033 962901 470622 757475 303519 365716 308262 527533 356597 781212 208651 215157 994512 > 3279 [i]