Best Known (82, 82+50, s)-Nets in Base 5
(82, 82+50, 252)-Net over F5 — Constructive and digital
Digital (82, 132, 252)-net over F5, using
- 12 times m-reduction [i] based on digital (82, 144, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 72, 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
- trace code for nets [i] based on digital (10, 72, 126)-net over F25, using
(82, 82+50, 352)-Net over F5 — Digital
Digital (82, 132, 352)-net over F5, using
(82, 82+50, 12459)-Net in Base 5 — Upper bound on s
There is no (82, 132, 12460)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 183 944929 356550 865695 947245 514726 890549 023071 351218 044072 554611 840618 287839 974180 339143 535537 > 5132 [i]