Best Known (82−64, 82, s)-Nets in Base 25
(82−64, 82, 126)-Net over F25 — Constructive and digital
Digital (18, 82, 126)-net over F25, using
- t-expansion [i] based on digital (10, 82, 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
(82−64, 82, 153)-Net over F25 — Digital
Digital (18, 82, 153)-net over F25, using
- net from sequence [i] based on digital (18, 152)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 18 and N(F) ≥ 153, using
(82−64, 82, 2019)-Net in Base 25 — Upper bound on s
There is no (18, 82, 2020)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 4 294862 467221 767037 455815 507689 529708 017025 020699 003698 267784 346152 612067 558263 962480 868716 028424 672231 358805 771265 > 2582 [i]