Best Known (41, 87, s)-Nets in Base 32
(41, 87, 218)-Net over F32 — Constructive and digital
Digital (41, 87, 218)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 30, 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 (11, 57, 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
- digital (7, 30, 98)-net over F32, using
(41, 87, 288)-Net in Base 32 — Constructive
(41, 87, 288)-net in base 32, using
- t-expansion [i] based on (40, 87, 288)-net in base 32, using
- 21 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
- 21 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
(41, 87, 468)-Net over F32 — Digital
Digital (41, 87, 468)-net over F32, using
(41, 87, 513)-Net in Base 32
(41, 87, 513)-net in base 32, using
- 1 times m-reduction [i] based on (41, 88, 513)-net in base 32, using
- base change [i] based on digital (8, 55, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 55, 513)-net over F256, using
(41, 87, 150125)-Net in Base 32 — Upper bound on s
There is no (41, 87, 150126)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 88734 345825 419495 369735 930549 321079 814594 064071 068147 619828 119882 716766 492410 109730 732072 498523 052900 536671 699768 480245 099453 762168 > 3287 [i]