Best Known (61−34, 61, s)-Nets in Base 32
(61−34, 61, 162)-Net over F32 — Constructive and digital
Digital (27, 61, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 20, 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, 41, 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, 20, 64)-net over F32, using
(61−34, 61, 261)-Net over F32 — Digital
Digital (27, 61, 261)-net over F32, using
(61−34, 61, 288)-Net in Base 32 — Constructive
(27, 61, 288)-net in base 32, using
- 2 times m-reduction [i] based on (27, 63, 288)-net in base 32, using
- base change [i] based on digital (9, 45, 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, 45, 288)-net over F128, using
(61−34, 61, 321)-Net in Base 32
(27, 61, 321)-net in base 32, using
- 5 times m-reduction [i] based on (27, 66, 321)-net in base 32, using
- base change [i] based on (16, 55, 321)-net in base 64, using
- 1 times m-reduction [i] based on (16, 56, 321)-net in base 64, using
- base change [i] based on digital (2, 42, 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, 42, 321)-net over F256, using
- 1 times m-reduction [i] based on (16, 56, 321)-net in base 64, using
- base change [i] based on (16, 55, 321)-net in base 64, using
(61−34, 61, 58257)-Net in Base 32 — Upper bound on s
There is no (27, 61, 58258)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 65 194086 988911 840606 882099 091729 631685 822460 991604 850443 426070 650866 540465 191691 657652 230935 > 3261 [i]