Best Known (69−48, 69, s)-Nets in Base 4
(69−48, 69, 34)-Net over F4 — Constructive and digital
Digital (21, 69, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
(69−48, 69, 44)-Net over F4 — Digital
Digital (21, 69, 44)-net over F4, using
- net from sequence [i] based on digital (21, 43)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 44, using
(69−48, 69, 134)-Net in Base 4 — Upper bound on s
There is no (21, 69, 135)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(469, 135, S4, 48), but
- the linear programming bound shows that M ≥ 698 947560 255739 804570 750882 828973 658730 894929 283364 690757 794924 473731 286309 609237 088634 527558 152535 528250 167793 854764 904638 681984 566783 195619 800970 235277 403521 294063 106409 896960 593207 432863 579316 475383 511105 146504 580874 033682 866948 229697 108640 576599 143493 552789 452572 597750 290952 059704 456830 271773 703036 692586 299392 / 1822 719559 683087 711560 963603 087289 719008 472261 068533 201675 872295 171635 991316 395469 457074 621945 314603 873199 616858 067310 901102 129328 252071 911179 358868 784939 323523 268420 781747 096481 541821 482396 186401 212301 359359 121864 891225 959212 867982 489211 916731 354191 751931 400313 914164 995223 > 469 [i]