Best Known (41, 110, s)-Nets in Base 32
(41, 110, 131)-Net over F32 — Constructive and digital
Digital (41, 110, 131)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 34, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (7, 76, 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 (0, 34, 33)-net over F32, using
(41, 110, 216)-Net in Base 32 — Constructive
(41, 110, 216)-net in base 32, using
- 322 times duplication [i] based on (39, 108, 216)-net in base 32, using
- t-expansion [i] based on (36, 108, 216)-net in base 32, using
- base change [i] based on (18, 90, 216)-net in base 64, using
- 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on (18, 90, 216)-net in base 64, using
- t-expansion [i] based on (36, 108, 216)-net in base 32, using
(41, 110, 308)-Net over F32 — Digital
Digital (41, 110, 308)-net over F32, using
- net from sequence [i] based on digital (41, 307)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 41 and N(F) ≥ 308, using
(41, 110, 342)-Net in Base 32
(41, 110, 342)-net in base 32, using
- 322 times duplication [i] based on (39, 108, 342)-net in base 32, using
- t-expansion [i] based on (38, 108, 342)-net in base 32, using
- base change [i] based on digital (20, 90, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- base change [i] based on digital (20, 90, 342)-net over F64, using
- t-expansion [i] based on (38, 108, 342)-net in base 32, using
(41, 110, 29186)-Net in Base 32 — Upper bound on s
There is no (41, 110, 29187)-net in base 32, because
- 1 times m-reduction [i] would yield (41, 109, 29187)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 115 205474 658751 330561 878115 374393 219361 149280 849575 716642 975210 312311 905265 840575 018843 670279 000580 261563 004973 213166 515923 852644 949268 020325 555635 114287 263253 816688 > 32109 [i]