Best Known (100, 100+45, s)-Nets in Base 5
(100, 100+45, 400)-Net over F5 — Constructive and digital
Digital (100, 145, 400)-net over F5, using
- 5 times m-reduction [i] based on digital (100, 150, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 75, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- trace code for nets [i] based on digital (25, 75, 200)-net over F25, using
(100, 100+45, 889)-Net over F5 — Digital
Digital (100, 145, 889)-net over F5, using
(100, 100+45, 85072)-Net in Base 5 — Upper bound on s
There is no (100, 145, 85073)-net in base 5, because
- 1 times m-reduction [i] would yield (100, 144, 85073)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 44850 607303 596597 533214 228223 615540 836506 374108 751067 497337 157036 099864 489459 334451 023417 557854 789321 > 5144 [i]