Best Known (144−99, 144, s)-Nets in Base 5
(144−99, 144, 78)-Net over F5 — Constructive and digital
Digital (45, 144, 78)-net over F5, using
- t-expansion [i] based on digital (38, 144, 78)-net over F5, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
(144−99, 144, 88)-Net over F5 — Digital
Digital (45, 144, 88)-net over F5, using
- net from sequence [i] based on digital (45, 87)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 45 and N(F) ≥ 88, using
(144−99, 144, 488)-Net in Base 5 — Upper bound on s
There is no (45, 144, 489)-net in base 5, because
- 1 times m-reduction [i] would yield (45, 143, 489)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 9545 951744 581399 767372 849000 879187 628069 879448 331653 684743 938951 242291 856535 876941 903557 983769 828325 > 5143 [i]