Best Known (30, 150, s)-Nets in Base 5
(30, 150, 51)-Net over F5 — Constructive and digital
Digital (30, 150, 51)-net over F5, using
- t-expansion [i] based on digital (22, 150, 51)-net over F5, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 22 and N(F) ≥ 51, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
(30, 150, 58)-Net over F5 — Digital
Digital (30, 150, 58)-net over F5, using
- net from sequence [i] based on digital (30, 57)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 30 and N(F) ≥ 58, using
(30, 150, 159)-Net over F5 — Upper bound on s (digital)
There is no digital (30, 150, 160)-net over F5, because
- extracting embedded orthogonal array [i] would yield linear OA(5150, 160, F5, 120) (dual of [160, 10, 121]-code), but
- construction Y1 [i] would yield
- linear OA(5149, 154, F5, 120) (dual of [154, 5, 121]-code), but
- residual code [i] would yield linear OA(529, 33, F5, 24) (dual of [33, 4, 25]-code), but
- OA(510, 160, S5, 6), but
- discarding factors would yield OA(510, 98, S5, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 9 810585 > 510 [i]
- discarding factors would yield OA(510, 98, S5, 6), but
- linear OA(5149, 154, F5, 120) (dual of [154, 5, 121]-code), but
- construction Y1 [i] would yield
(30, 150, 281)-Net in Base 5 — Upper bound on s
There is no (30, 150, 282)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 747 766952 534899 732021 227558 299341 701123 132692 986855 085274 688462 880787 213360 997757 395655 234257 666059 423425 > 5150 [i]