Best Known (31, 67, s)-Nets in Base 32
(31, 67, 174)-Net over F32 — Constructive and digital
Digital (31, 67, 174)-net over F32, using
- 2 times m-reduction [i] based on digital (31, 69, 174)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 24, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (7, 45, 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 (5, 24, 76)-net over F32, using
- (u, u+v)-construction [i] based on
(31, 67, 288)-Net in Base 32 — Constructive
(31, 67, 288)-net in base 32, using
- 10 times m-reduction [i] based on (31, 77, 288)-net in base 32, using
- base change [i] based on digital (9, 55, 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, 55, 288)-net over F128, using
(31, 67, 350)-Net over F32 — Digital
Digital (31, 67, 350)-net over F32, using
(31, 67, 97550)-Net in Base 32 — Upper bound on s
There is no (31, 67, 97551)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 69995 184884 226013 410336 872275 445551 309608 440907 192600 305816 537034 475169 066992 974251 109075 632650 334704 > 3267 [i]