Best Known (19, 19+43, s)-Nets in Base 4
(19, 19+43, 33)-Net over F4 — Constructive and digital
Digital (19, 62, 33)-net over F4, using
- t-expansion [i] based on digital (15, 62, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
(19, 19+43, 41)-Net over F4 — Digital
Digital (19, 62, 41)-net over F4, using
- t-expansion [i] based on digital (18, 62, 41)-net over F4, using
- net from sequence [i] based on digital (18, 40)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 18 and N(F) ≥ 41, using
- net from sequence [i] based on digital (18, 40)-sequence over F4, using
(19, 19+43, 129)-Net in Base 4 — Upper bound on s
There is no (19, 62, 130)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(462, 130, S4, 43), but
- the linear programming bound shows that M ≥ 4019 078744 078071 827932 976683 558087 106372 035655 553747 017450 560398 815316 874632 749975 367234 727517 108611 722285 782813 728407 121836 637500 182422 765574 307752 283228 460101 184880 165144 200806 158609 438983 358128 411916 632064 / 188 119748 538951 428307 632682 475057 886108 439303 255341 851012 879539 112075 808835 961217 242169 809210 626046 940984 309082 261094 059915 883134 270392 288329 037536 921218 642905 933928 040633 > 462 [i]