Best Known (59−45, 59, s)-Nets in Base 5
(59−45, 59, 35)-Net over F5 — Constructive and digital
Digital (14, 59, 35)-net over F5, using
- net from sequence [i] based on digital (14, 34)-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 3 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]
(59−45, 59, 39)-Net over F5 — Digital
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
(59−45, 59, 114)-Net in Base 5 — Upper bound on s
There is no (14, 59, 115)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(559, 115, S5, 45), but
- the linear programming bound shows that M ≥ 2052 177576 631715 933395 592865 639272 479277 138082 597030 213510 946688 833505 548815 926680 143563 085136 500038 615722 848833 502360 721238 921255 576826 937164 421823 951709 900057 949198 526330 292224 884033 203125 / 10496 278813 914454 735328 620622 221536 930889 445591 344402 375842 867977 045174 713471 763017 664403 600049 158830 810997 230877 196171 161301 294335 992078 191304 870011 > 559 [i]