Best Known (15, 15+19, s)-Nets in Base 4
(15, 15+19, 33)-Net over F4 — Constructive and digital
Digital (15, 34, 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
(15, 15+19, 35)-Net over F4 — Digital
Digital (15, 34, 35)-net over F4, using
- net from sequence [i] based on digital (15, 34)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 35, using
(15, 15+19, 216)-Net in Base 4 — Upper bound on s
There is no (15, 34, 217)-net in base 4, because
- 1 times m-reduction [i] would yield (15, 33, 217)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 76 749341 876169 173452 > 433 [i]