Best Known (15, 15+37, s)-Nets in Base 4
(15, 15+37, 33)-Net over F4 — Constructive and digital
Digital (15, 52, 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
(15, 15+37, 35)-Net over F4 — Digital
Digital (15, 52, 35)-net over F4, using
- net from sequence [i] based on digital (15, 34)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 35, using
(15, 15+37, 99)-Net in Base 4 — Upper bound on s
There is no (15, 52, 100)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(452, 100, S4, 37), but
- the linear programming bound shows that M ≥ 122286 562316 677400 710065 247950 699724 199256 311251 272039 790450 228019 543203 578727 206911 566962 340550 130811 972817 601855 688395 354953 747543 223204 680493 432832 / 5909 445624 660275 177735 061262 841863 583710 628534 785955 840883 780789 693140 214269 486067 169858 699936 055397 157033 616741 653933 > 452 [i]