Best Known (59−41, 59, s)-Nets in Base 4
(59−41, 59, 33)-Net over F4 — Constructive and digital
Digital (18, 59, 33)-net over F4, using
- t-expansion [i] based on digital (15, 59, 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
(59−41, 59, 41)-Net over F4 — Digital
Digital (18, 59, 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
(59−41, 59, 124)-Net in Base 4 — Upper bound on s
There is no (18, 59, 125)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(459, 125, S4, 41), but
- the linear programming bound shows that M ≥ 6 098659 704705 486904 667441 402011 989050 548288 910427 912825 765842 283670 760248 415348 522730 039189 577335 282788 475369 967101 883338 375933 306396 897634 126855 141698 525692 111751 859853 590528 / 17 865783 539531 952003 937094 580988 623442 037272 256331 005047 247373 356459 142621 652981 139301 072409 181322 127802 625025 609129 027701 857126 610015 951793 > 459 [i]