Best Known (78−58, 78, s)-Nets in Base 4
(78−58, 78, 33)-Net over F4 — Constructive and digital
Digital (20, 78, 33)-net over F4, using
- t-expansion [i] based on digital (15, 78, 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
(78−58, 78, 41)-Net over F4 — Digital
Digital (20, 78, 41)-net over F4, using
- t-expansion [i] based on digital (18, 78, 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
(78−58, 78, 89)-Net in Base 4 — Upper bound on s
There is no (20, 78, 90)-net in base 4, because
- 1 times m-reduction [i] would yield (20, 77, 90)-net in base 4, but
- extracting embedded orthogonal array [i] would yield OA(477, 90, S4, 57), but
- the linear programming bound shows that M ≥ 812 594910 355982 022521 248766 990253 358928 698493 894656 / 29029 > 477 [i]
- extracting embedded orthogonal array [i] would yield OA(477, 90, S4, 57), but