Best Known (16, 16+69, s)-Nets in Base 25
(16, 16+69, 126)-Net over F25 — Constructive and digital
Digital (16, 85, 126)-net over F25, using
- t-expansion [i] based on digital (10, 85, 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
(16, 16+69, 150)-Net over F25 — Digital
Digital (16, 85, 150)-net over F25, using
- net from sequence [i] based on digital (16, 149)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 16 and N(F) ≥ 150, using
(16, 16+69, 1585)-Net in Base 25 — Upper bound on s
There is no (16, 85, 1586)-net in base 25, because
- 1 times m-reduction [i] would yield (16, 84, 1586)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 2708 842868 422192 859962 668951 257710 528840 242803 601361 293358 289336 512624 059824 773400 338214 455765 408451 751359 314213 967905 > 2584 [i]