Best Known (69−38, 69, s)-Nets in Base 32
(69−38, 69, 174)-Net over F32 — Constructive and digital
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
(69−38, 69, 288)-Net in Base 32 — Constructive
(31, 69, 288)-net in base 32, using
- 8 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
(69−38, 69, 306)-Net over F32 — Digital
Digital (31, 69, 306)-net over F32, using
(69−38, 69, 321)-Net in Base 32
(31, 69, 321)-net in base 32, using
- 8 times m-reduction [i] based on (31, 77, 321)-net in base 32, using
- base change [i] based on (9, 55, 321)-net in base 128, using
- 1 times m-reduction [i] based on (9, 56, 321)-net in base 128, using
- base change [i] based on digital (2, 49, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 49, 321)-net over F256, using
- 1 times m-reduction [i] based on (9, 56, 321)-net in base 128, using
- base change [i] based on (9, 55, 321)-net in base 128, using
(69−38, 69, 74794)-Net in Base 32 — Upper bound on s
There is no (31, 69, 74795)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 71 683095 181292 065024 393408 574198 866777 018857 259487 436228 142728 373115 193131 182727 767246 171818 911427 149808 > 3269 [i]