Best Known (68−52, 68, s)-Nets in Base 5
(68−52, 68, 37)-Net over F5 — Constructive and digital
Digital (16, 68, 37)-net over F5, using
- net from sequence [i] based on digital (16, 36)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 5 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(68−52, 68, 40)-Net over F5 — Digital
Digital (16, 68, 40)-net over F5, using
- net from sequence [i] based on digital (16, 39)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 16 and N(F) ≥ 40, using
(68−52, 68, 115)-Net in Base 5 — Upper bound on s
There is no (16, 68, 116)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(568, 116, S5, 52), but
- the linear programming bound shows that M ≥ 11 600142 638871 168869 792982 455632 271705 664267 734631 082588 063519 777161 754196 145898 834866 089731 863991 740823 394138 715229 928493 499755 859375 / 33 956206 214369 087048 603401 189650 732303 281056 656666 162934 916265 145737 078434 374641 908943 > 568 [i]