Best Known (68−63, 68, s)-Nets in Base 5
(68−63, 68, 20)-Net over F5 — Constructive and digital
Digital (5, 68, 20)-net over F5, using
- net from sequence [i] based on digital (5, 19)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 5 and N(F) ≥ 20, using
(68−63, 68, 31)-Net in Base 5 — Upper bound on s
There is no (5, 68, 32)-net in base 5, because
- 8 times m-reduction [i] would yield (5, 60, 32)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(560, 32, S5, 2, 55), but
- the LP bound with quadratic polynomials shows that M ≥ 25 153490 401663 702868 972904 980182 647705 078125 / 28 > 560 [i]
- extracting embedded OOA [i] would yield OOA(560, 32, S5, 2, 55), but