Best Known (41, 41+52, s)-Nets in Base 32
(41, 41+52, 196)-Net over F32 — Constructive and digital
Digital (41, 93, 196)-net over F32, using
- 2 times m-reduction [i] based on digital (41, 95, 196)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 34, 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 (7, 61, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 34, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(41, 41+52, 288)-Net in Base 32 — Constructive
(41, 93, 288)-net in base 32, using
- t-expansion [i] based on (40, 93, 288)-net in base 32, using
- 15 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
- 15 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
(41, 41+52, 350)-Net over F32 — Digital
Digital (41, 93, 350)-net over F32, using
(41, 41+52, 408)-Net in Base 32
(41, 93, 408)-net in base 32, using
- 3 times m-reduction [i] based on (41, 96, 408)-net in base 32, using
- base change [i] based on digital (25, 80, 408)-net over F64, using
- net from sequence [i] based on digital (25, 407)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 25 and N(F) ≥ 408, using
- net from sequence [i] based on digital (25, 407)-sequence over F64, using
- base change [i] based on digital (25, 80, 408)-net over F64, using
(41, 41+52, 82350)-Net in Base 32 — Upper bound on s
There is no (41, 93, 82351)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 95 280617 126438 384270 836144 821851 436666 095196 209780 053967 495252 552809 687289 583618 538494 490313 679068 374229 068908 647468 541607 989084 782858 518882 > 3293 [i]