Best Known (10, 10+21, s)-Nets in Base 8
(10, 10+21, 46)-Net over F8 — Constructive and digital
Digital (10, 31, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
(10, 10+21, 325)-Net in Base 8 — Upper bound on s
There is no (10, 31, 326)-net in base 8, because
- 1 times m-reduction [i] would yield (10, 30, 326)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1262 450662 382914 877214 720624 > 830 [i]