Best Known (99−61, 99, s)-Nets in Base 32
(99−61, 99, 142)-Net over F32 — Constructive and digital
Digital (38, 99, 142)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 31, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (7, 68, 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 (1, 31, 44)-net over F32, using
(99−61, 99, 288)-Net in Base 32 — Constructive
(38, 99, 288)-net in base 32, using
- 321 times duplication [i] based on (37, 98, 288)-net in base 32, using
- base change [i] based on digital (9, 70, 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, 70, 288)-net over F128, using
(99−61, 99, 291)-Net over F32 — Digital
Digital (38, 99, 291)-net over F32, using
- net from sequence [i] based on digital (38, 290)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 38 and N(F) ≥ 291, using
(99−61, 99, 342)-Net in Base 32
(38, 99, 342)-net in base 32, using
- 9 times m-reduction [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
(99−61, 99, 32065)-Net in Base 32 — Upper bound on s
There is no (38, 99, 32066)-net in base 32, because
- 1 times m-reduction [i] would yield (38, 98, 32066)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 3197 547169 360972 003740 638592 063534 990039 780579 813194 582944 699044 400135 044837 983188 407157 883494 675585 263093 565427 649326 859811 546556 737984 527732 154720 > 3298 [i]