Best Known (91−22, 91, s)-Nets in Base 7
(91−22, 91, 1527)-Net over F7 — Constructive and digital
Digital (69, 91, 1527)-net over F7, using
- net defined by OOA [i] based on linear OOA(791, 1527, F7, 22, 22) (dual of [(1527, 22), 33503, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(791, 16797, F7, 22) (dual of [16797, 16706, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(791, 16797, F7, 22) (dual of [16797, 16706, 23]-code), using
(91−22, 91, 8780)-Net over F7 — Digital
Digital (69, 91, 8780)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(791, 8780, F7, 22) (dual of [8780, 8689, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using
(91−22, 91, 8019146)-Net in Base 7 — Upper bound on s
There is no (69, 91, 8019147)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 80153 414570 251208 067801 825538 214901 363464 348238 521419 437620 052557 596654 723903 > 791 [i]