Best Known (17, 17+199, s)-Nets in Base 4
(17, 17+199, 33)-Net over F4 — Constructive and digital
Digital (17, 216, 33)-net over F4, using
- t-expansion [i] based on digital (15, 216, 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
(17, 17+199, 40)-Net over F4 — Digital
Digital (17, 216, 40)-net over F4, using
- net from sequence [i] based on digital (17, 39)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 17 and N(F) ≥ 40, using
(17, 17+199, 62)-Net in Base 4 — Upper bound on s
There is no (17, 216, 63)-net in base 4, because
- 31 times m-reduction [i] would yield (17, 185, 63)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4185, 63, S4, 3, 168), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 413644 108018 789698 761718 438551 312351 957624 215974 124562 187933 744234 024911 175385 755930 374377 187512 542127 608643 452928 / 169 > 4185 [i]
- extracting embedded OOA [i] would yield OOA(4185, 63, S4, 3, 168), but