Best Known (68, 90, s)-Nets in Base 7
(68, 90, 763)-Net over F7 — Constructive and digital
Digital (68, 90, 763)-net over F7, using
- net defined by OOA [i] based on linear OOA(790, 763, F7, 22, 22) (dual of [(763, 22), 16696, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(790, 8393, F7, 22) (dual of [8393, 8303, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(790, 8403, F7, 22) (dual of [8403, 8313, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(790, 8393, F7, 22) (dual of [8393, 8303, 23]-code), using
(68, 90, 7965)-Net over F7 — Digital
Digital (68, 90, 7965)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(790, 7965, F7, 22) (dual of [7965, 7875, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(790, 8403, F7, 22) (dual of [8403, 8313, 23]-code), using
(68, 90, 6718943)-Net in Base 7 — Upper bound on s
There is no (68, 90, 6718944)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 11450 491542 779306 144423 577944 160873 048010 207879 285082 818345 533348 584778 223105 > 790 [i]