Best Known (80−43, 80, s)-Nets in Base 32
(80−43, 80, 202)-Net over F32 — Constructive and digital
Digital (37, 80, 202)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 28, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (9, 52, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (7, 28, 98)-net over F32, using
(80−43, 80, 288)-Net in Base 32 — Constructive
(37, 80, 288)-net in base 32, using
- 18 times m-reduction [i] based on (37, 98, 288)-net in base 32, using
- base change [i] based on digital (9, 70, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 70, 288)-net over F128, using
(80−43, 80, 397)-Net over F32 — Digital
Digital (37, 80, 397)-net over F32, using
(80−43, 80, 128625)-Net in Base 32 — Upper bound on s
There is no (37, 80, 128626)-net in base 32, because
- 1 times m-reduction [i] would yield (37, 79, 128626)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 80707 285502 199324 713311 070524 914116 038780 735475 551428 364333 401975 009793 703475 589367 544173 098132 434425 713151 150267 287432 > 3279 [i]