Best Known (61−43, 61, s)-Nets in Base 4
(61−43, 61, 33)-Net over F4 — Constructive and digital
Digital (18, 61, 33)-net over F4, using
- t-expansion [i] based on digital (15, 61, 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
(61−43, 61, 41)-Net over F4 — Digital
Digital (18, 61, 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
(61−43, 61, 114)-Net in Base 4 — Upper bound on s
There is no (18, 61, 115)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(461, 115, S4, 43), but
- the linear programming bound shows that M ≥ 8 867577 820394 892078 302903 376011 219649 893047 268294 051459 959774 715216 956970 670840 325873 158120 379501 398960 032970 458008 737468 823847 270763 370822 590292 322808 758272 / 1 568698 363933 661749 730985 011129 979312 182529 988673 402786 941022 163461 443141 672915 973490 090934 276533 827022 911521 994930 215625 > 461 [i]