Best Known (125−89, 125, s)-Nets in Base 5
(125−89, 125, 72)-Net over F5 — Constructive and digital
Digital (36, 125, 72)-net over F5, using
- t-expansion [i] based on digital (31, 125, 72)-net over F5, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 31 and N(F) ≥ 72, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
(125−89, 125, 76)-Net over F5 — Digital
Digital (36, 125, 76)-net over F5, using
- t-expansion [i] based on digital (34, 125, 76)-net over F5, using
- net from sequence [i] based on digital (34, 75)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 34 and N(F) ≥ 76, using
- net from sequence [i] based on digital (34, 75)-sequence over F5, using
(125−89, 125, 370)-Net in Base 5 — Upper bound on s
There is no (36, 125, 371)-net in base 5, because
- 1 times m-reduction [i] would yield (36, 124, 371)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 479 223872 772879 848324 248636 567524 879646 267057 297596 995625 131507 126592 222957 804881 802705 > 5124 [i]