Best Known (15, 47, s)-Nets in Base 4
(15, 47, 33)-Net over F4 — Constructive and digital
Digital (15, 47, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
(15, 47, 35)-Net over F4 — Digital
Digital (15, 47, 35)-net over F4, using
- net from sequence [i] based on digital (15, 34)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 35, using
(15, 47, 120)-Net in Base 4 — Upper bound on s
There is no (15, 47, 121)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 20631 330572 304362 432028 827629 > 447 [i]
- extracting embedded orthogonal array [i] would yield OA(447, 121, S4, 32), but
- the linear programming bound shows that M ≥ 365 129709 190376 390301 373618 637040 010384 793045 585047 102752 276086 784000 / 18163 087858 506659 594163 938688 475283 050507 > 447 [i]