Best Known (114−47, 114, s)-Nets in Base 5
(114−47, 114, 252)-Net over F5 — Constructive and digital
Digital (67, 114, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 57, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(114−47, 114, 6387)-Net in Base 5 — Upper bound on s
There is no (67, 114, 6388)-net in base 5, because
- 1 times m-reduction [i] would yield (67, 113, 6388)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 9 647415 618012 634336 530650 751543 367548 237238 980016 017552 496048 743796 612693 708625 > 5113 [i]