Best Known (110−67, 110, s)-Nets in Base 32
(110−67, 110, 162)-Net over F32 — Constructive and digital
Digital (43, 110, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 36, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (7, 74, 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 (3, 36, 64)-net over F32, using
(110−67, 110, 288)-Net in Base 32 — Constructive
(43, 110, 288)-net in base 32, using
- 322 times duplication [i] based on (41, 108, 288)-net in base 32, using
- t-expansion [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
- t-expansion [i] based on (40, 108, 288)-net in base 32, using
(110−67, 110, 308)-Net over F32 — Digital
Digital (43, 110, 308)-net over F32, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (41, 307)-sequence over F32, using
(110−67, 110, 342)-Net in Base 32
(43, 110, 342)-net in base 32, using
- 322 times duplication [i] based on (41, 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
(110−67, 110, 39752)-Net in Base 32 — Upper bound on s
There is no (43, 110, 39753)-net in base 32, because
- 1 times m-reduction [i] would yield (43, 109, 39753)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 115 241099 031399 525985 367917 449345 918152 352860 909160 155644 874193 988485 562004 763074 179119 901003 240024 729483 713982 226109 128808 982306 474985 119597 081913 797366 200942 866512 > 32109 [i]