Best Known (59−44, 59, s)-Nets in Base 5
(59−44, 59, 36)-Net over F5 — Constructive and digital
Digital (15, 59, 36)-net over F5, using
- net from sequence [i] based on digital (15, 35)-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 4 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]
(59−44, 59, 39)-Net over F5 — Digital
Digital (15, 59, 39)-net over F5, using
- t-expansion [i] based on digital (14, 59, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
(59−44, 59, 136)-Net in Base 5 — Upper bound on s
There is no (15, 59, 137)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(559, 137, S5, 44), but
- the linear programming bound shows that M ≥ 6 419517 641433 319175 277551 883830 561130 235282 164732 919263 152800 726898 975265 543431 840833 990841 044939 038212 597637 570632 295245 258161 391004 106399 726936 160732 293501 496315 002441 406250 / 36 159839 840037 061904 111392 029142 393798 113966 279889 575250 749951 379331 378086 540435 820788 921595 503877 713000 021822 021770 474969 914355 972857 > 559 [i]