Best Known (8, 8+7, s)-Nets in Base 4
(8, 8+7, 37)-Net over F4 — Constructive and digital
Digital (8, 15, 37)-net over F4, using
- (u, u+v)-construction [i] based on
(8, 8+7, 42)-Net over F4 — Digital
Digital (8, 15, 42)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(415, 42, F4, 2, 7) (dual of [(42, 2), 69, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(415, 84, F4, 7) (dual of [84, 69, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(415, 85, F4, 7) (dual of [85, 70, 8]-code), using
- OOA 2-folding [i] based on linear OA(415, 84, F4, 7) (dual of [84, 69, 8]-code), using
(8, 8+7, 388)-Net in Base 4 — Upper bound on s
There is no (8, 15, 389)-net in base 4, because
- 1 times m-reduction [i] would yield (8, 14, 389)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 268 985332 > 414 [i]