Best Known (26, 26+9, s)-Nets in Base 7
(26, 26+9, 2100)-Net over F7 — Constructive and digital
Digital (26, 35, 2100)-net over F7, using
- net defined by OOA [i] based on linear OOA(735, 2100, F7, 9, 9) (dual of [(2100, 9), 18865, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(735, 8401, F7, 9) (dual of [8401, 8366, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(735, 8403, F7, 9) (dual of [8403, 8368, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(735, 8401, F7, 9) (dual of [8401, 8366, 10]-code), using
(26, 26+9, 7167)-Net over F7 — Digital
Digital (26, 35, 7167)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(735, 7167, F7, 9) (dual of [7167, 7132, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(735, 8403, F7, 9) (dual of [8403, 8368, 10]-code), using
(26, 26+9, 5626453)-Net in Base 7 — Upper bound on s
There is no (26, 35, 5626454)-net in base 7, because
- 1 times m-reduction [i] would yield (26, 34, 5626454)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 54116 975800 941953 388474 150697 > 734 [i]