Best Known (89−21, 89, s)-Nets in Base 7
(89−21, 89, 840)-Net over F7 — Constructive and digital
Digital (68, 89, 840)-net over F7, using
- net defined by OOA [i] based on linear OOA(789, 840, F7, 21, 21) (dual of [(840, 21), 17551, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(789, 8401, F7, 21) (dual of [8401, 8312, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(789, 8402, F7, 21) (dual of [8402, 8313, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(789, 8401, F7, 21) (dual of [8401, 8312, 22]-code), using
(89−21, 89, 8402)-Net over F7 — Digital
Digital (68, 89, 8402)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(789, 8402, F7, 21) (dual of [8402, 8313, 22]-code), using
(89−21, 89, large)-Net in Base 7 — Upper bound on s
There is no (68, 89, large)-net in base 7, because
- 19 times m-reduction [i] would yield (68, 70, large)-net in base 7, but