Best Known (64−44, 64, s)-Nets in Base 4
(64−44, 64, 33)-Net over F4 — Constructive and digital
Digital (20, 64, 33)-net over F4, using
- t-expansion [i] based on digital (15, 64, 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
(64−44, 64, 41)-Net over F4 — Digital
Digital (20, 64, 41)-net over F4, using
- t-expansion [i] based on digital (18, 64, 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
(64−44, 64, 139)-Net in Base 4 — Upper bound on s
There is no (20, 64, 140)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(464, 140, S4, 44), but
- the linear programming bound shows that M ≥ 6 055971 130979 717035 237533 763765 896035 104411 078322 823391 498324 273826 156962 484218 588303 215205 346683 113225 234756 746893 442044 988412 906254 866058 803915 928912 265216 000000 / 17465 630993 245964 374557 288355 588936 264526 909741 890553 067641 295523 141418 950639 065672 191422 532782 852686 274622 640710 777054 531879 > 464 [i]