Best Known (19, 19+45, s)-Nets in Base 4
(19, 19+45, 33)-Net over F4 — Constructive and digital
Digital (19, 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
(19, 19+45, 41)-Net over F4 — Digital
Digital (19, 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
(19, 19+45, 118)-Net in Base 4 — Upper bound on s
There is no (19, 64, 119)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(464, 119, S4, 45), but
- the linear programming bound shows that M ≥ 86281 259132 858652 351318 621152 193776 169011 314302 048568 574075 512291 106476 673632 920228 434592 062075 337852 335348 631534 055263 738553 834940 174592 676821 962753 440810 532864 / 242 561963 734980 780383 061022 729662 792650 160301 201736 163590 343831 386934 538599 980695 527882 064362 246641 801684 355864 415256 969895 > 464 [i]