Best Known (72, 148, s)-Nets in Base 5
(72, 148, 88)-Net over F5 — Constructive and digital
Digital (72, 148, 88)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (3, 41, 16)-net over F5, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 3 and N(F) ≥ 16, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- digital (31, 107, 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
- digital (3, 41, 16)-net over F5, using
(72, 148, 132)-Net over F5 — Digital
Digital (72, 148, 132)-net over F5, using
- t-expansion [i] based on digital (67, 148, 132)-net over F5, using
- net from sequence [i] based on digital (67, 131)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 67 and N(F) ≥ 132, using
- net from sequence [i] based on digital (67, 131)-sequence over F5, using
(72, 148, 1953)-Net in Base 5 — Upper bound on s
There is no (72, 148, 1954)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 28 088629 062395 947206 732246 439137 152193 204135 014108 141021 207883 585991 069684 508126 742837 145211 915800 553985 > 5148 [i]