Best Known (13, 53, s)-Nets in Base 5
(13, 53, 34)-Net over F5 — Constructive and digital
Digital (13, 53, 34)-net over F5, using
- net from sequence [i] based on digital (13, 33)-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 2 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]
(13, 53, 36)-Net over F5 — Digital
Digital (13, 53, 36)-net over F5, using
- net from sequence [i] based on digital (13, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 13 and N(F) ≥ 36, using
(13, 53, 117)-Net in Base 5 — Upper bound on s
There is no (13, 53, 118)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(553, 118, S5, 40), but
- the linear programming bound shows that M ≥ 1096 668006 375589 366723 890605 201278 526057 221738 726032 568860 206504 210762 340563 163007 725188 517483 692622 437959 189681 020072 626438 377483 282238 245010 375976 562500 / 97 510161 475974 122552 396197 804181 728556 038193 197940 285024 983209 979941 480797 033648 403539 858860 172963 436093 402267 710189 > 553 [i]