Best Known (66−57, 66, s)-Nets in Base 32
(66−57, 66, 104)-Net over F32 — Constructive and digital
Digital (9, 66, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
(66−57, 66, 108)-Net over F32 — Digital
Digital (9, 66, 108)-net over F32, using
- net from sequence [i] based on digital (9, 107)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 108, using
(66−57, 66, 1122)-Net in Base 32 — Upper bound on s
There is no (9, 66, 1123)-net in base 32, because
- 1 times m-reduction [i] would yield (9, 65, 1123)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 69 050576 851522 346100 690585 143218 335941 653911 284641 884933 343120 474833 556806 534289 396715 935495 666808 > 3265 [i]