Best Known (15, 15+47, s)-Nets in Base 5
(15, 15+47, 36)-Net over F5 — Constructive and digital
Digital (15, 62, 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]
(15, 15+47, 39)-Net over F5 — Digital
Digital (15, 62, 39)-net over F5, using
- t-expansion [i] based on digital (14, 62, 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
(15, 15+47, 122)-Net in Base 5 — Upper bound on s
There is no (15, 62, 123)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(562, 123, S5, 47), but
- the linear programming bound shows that M ≥ 866789 265999 481006 995111 931622 668020 955157 670303 851192 839270 543498 383039 028227 400179 546930 020591 083271 027599 271945 575395 568792 715347 523763 234109 346024 514887 438636 141234 184757 538554 916278 528139 628178 905695 676803 588867 187500 / 39510 101523 934728 320459 161161 952060 595184 156530 011721 934959 719219 576447 028061 207348 686856 690578 470594 842937 145430 897644 980686 177007 629890 864027 357783 091690 843394 520716 854095 337293 > 562 [i]