Best Known (6, 6+78, s)-Nets in Base 32
(6, 6+78, 76)-Net over F32 — Constructive and digital
Digital (6, 84, 76)-net over F32, using
- t-expansion [i] based on digital (5, 84, 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
(6, 6+78, 86)-Net over F32 — Digital
Digital (6, 84, 86)-net over F32, using
- net from sequence [i] based on digital (6, 85)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 6 and N(F) ≥ 86, using
(6, 6+78, 757)-Net in Base 32 — Upper bound on s
There is no (6, 84, 758)-net in base 32, because
- 30 times m-reduction [i] would yield (6, 54, 758)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1900 564278 265475 535120 279426 588986 150981 626152 759275 234162 677226 755533 557655 126892 > 3254 [i]