Best Known (70−17, 70, s)-Nets in Base 7
(70−17, 70, 1050)-Net over F7 — Constructive and digital
Digital (53, 70, 1050)-net over F7, using
- net defined by OOA [i] based on linear OOA(770, 1050, F7, 17, 17) (dual of [(1050, 17), 17780, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(770, 8401, F7, 17) (dual of [8401, 8331, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(770, 8403, F7, 17) (dual of [8403, 8333, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(770, 8401, F7, 17) (dual of [8401, 8331, 18]-code), using
(70−17, 70, 8253)-Net over F7 — Digital
Digital (53, 70, 8253)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(770, 8253, F7, 17) (dual of [8253, 8183, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(770, 8403, F7, 17) (dual of [8403, 8333, 18]-code), using
(70−17, 70, large)-Net in Base 7 — Upper bound on s
There is no (53, 70, large)-net in base 7, because
- 15 times m-reduction [i] would yield (53, 55, large)-net in base 7, but