Best Known (42, 42+52, s)-Nets in Base 32
(42, 42+52, 202)-Net over F32 — Constructive and digital
Digital (42, 94, 202)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 33, 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, 61, 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, 33, 98)-net over F32, using
(42, 42+52, 288)-Net in Base 32 — Constructive
(42, 94, 288)-net in base 32, using
- t-expansion [i] based on (40, 94, 288)-net in base 32, using
- 14 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
- base change [i] based on (22, 90, 288)-net in base 64, using
- 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 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, 78, 288)-net over F128, using
- 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on (22, 90, 288)-net in base 64, using
- 14 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
(42, 42+52, 376)-Net over F32 — Digital
Digital (42, 94, 376)-net over F32, using
(42, 42+52, 425)-Net in Base 32
(42, 94, 425)-net in base 32, using
- 2 times m-reduction [i] based on (42, 96, 425)-net in base 32, using
- base change [i] based on digital (26, 80, 425)-net over F64, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 26 and N(F) ≥ 425, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- base change [i] based on digital (26, 80, 425)-net over F64, using
(42, 42+52, 94094)-Net in Base 32 — Upper bound on s
There is no (42, 94, 94095)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 3048 707384 710926 293666 727699 393158 065997 420990 684821 595264 392516 799727 772400 781653 497017 376675 158314 227581 705194 987773 361090 129788 212194 189080 > 3294 [i]