Best Known (12−7, 12, s)-Nets in Base 8
(12−7, 12, 28)-Net over F8 — Constructive and digital
Digital (5, 12, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
(12−7, 12, 33)-Net in Base 8 — Constructive
(5, 12, 33)-net in base 8, using
- base change [i] based on digital (2, 9, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
(12−7, 12, 36)-Net over F8 — Digital
Digital (5, 12, 36)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(812, 36, F8, 2, 7) (dual of [(36, 2), 60, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(812, 72, F8, 7) (dual of [72, 60, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(812, 73, F8, 7) (dual of [73, 61, 8]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(812, 73, F8, 7) (dual of [73, 61, 8]-code), using
- OOA 2-folding [i] based on linear OA(812, 72, F8, 7) (dual of [72, 60, 8]-code), using
(12−7, 12, 530)-Net in Base 8 — Upper bound on s
There is no (5, 12, 531)-net in base 8, because
- 1 times m-reduction [i] would yield (5, 11, 531)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 8628 258472 > 811 [i]