Best Known (102−33, 102, s)-Nets in Base 4
(102−33, 102, 240)-Net over F4 — Constructive and digital
Digital (69, 102, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 34, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
(102−33, 102, 358)-Net over F4 — Digital
Digital (69, 102, 358)-net over F4, using
(102−33, 102, 14306)-Net in Base 4 — Upper bound on s
There is no (69, 102, 14307)-net in base 4, because
- 1 times m-reduction [i] would yield (69, 101, 14307)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 6 431699 248576 560432 232549 529929 156142 180206 086522 613951 264186 > 4101 [i]