Best Known (63−48, 63, s)-Nets in Base 5
(63−48, 63, 36)-Net over F5 — Constructive and digital
Digital (15, 63, 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]
(63−48, 63, 39)-Net over F5 — Digital
Digital (15, 63, 39)-net over F5, using
- t-expansion [i] based on digital (14, 63, 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
(63−48, 63, 117)-Net in Base 5 — Upper bound on s
There is no (15, 63, 118)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(563, 118, S5, 48), but
- the linear programming bound shows that M ≥ 17 594971 096394 584317 413754 907816 525470 016082 106496 860763 635903 224586 366035 110124 184139 525871 368793 484307 683395 486008 621931 338037 569599 658886 296973 629302 826946 929627 638382 953591 644763 946533 203125 / 147783 644821 837289 945423 876998 652832 650155 785782 921141 199040 852619 822364 042096 097476 791664 657775 311104 165472 217625 400396 249324 100719 831903 908037 631029 > 563 [i]