Best Known (7, 7+9, s)-Nets in Base 5
(7, 7+9, 24)-Net over F5 — Constructive and digital
Digital (7, 16, 24)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 12)-net over F5, using
- digital (2, 11, 12)-net over F5, using
- net from sequence [i] based on digital (2, 11)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 2 and N(F) ≥ 12, using
- net from sequence [i] based on digital (2, 11)-sequence over F5, using
(7, 7+9, 26)-Net over F5 — Digital
Digital (7, 16, 26)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(516, 26, F5, 2, 9) (dual of [(26, 2), 36, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(516, 52, F5, 9) (dual of [52, 36, 10]-code), using
- a “LX†code from Brouwer’s database [i]
- OOA 2-folding [i] based on linear OA(516, 52, F5, 9) (dual of [52, 36, 10]-code), using
(7, 7+9, 228)-Net in Base 5 — Upper bound on s
There is no (7, 16, 229)-net in base 5, because
- 1 times m-reduction [i] would yield (7, 15, 229)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 30630 347505 > 515 [i]