Best Known (92−22, 92, s)-Nets in Base 7
(92−22, 92, 1528)-Net over F7 — Constructive and digital
Digital (70, 92, 1528)-net over F7, using
- net defined by OOA [i] based on linear OOA(792, 1528, F7, 22, 22) (dual of [(1528, 22), 33524, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(792, 16808, F7, 22) (dual of [16808, 16716, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(792, 16813, F7, 22) (dual of [16813, 16721, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] 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]
- linear OA(786, 16807, F7, 20) (dual of [16807, 16721, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(71, 6, F7, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(792, 16813, F7, 22) (dual of [16813, 16721, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(792, 16808, F7, 22) (dual of [16808, 16716, 23]-code), using
(92−22, 92, 9678)-Net over F7 — Digital
Digital (70, 92, 9678)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(792, 9678, F7, 22) (dual of [9678, 9586, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(792, 16813, F7, 22) (dual of [16813, 16721, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] 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]
- linear OA(786, 16807, F7, 20) (dual of [16807, 16721, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(71, 6, F7, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(792, 16813, F7, 22) (dual of [16813, 16721, 23]-code), using
(92−22, 92, large)-Net in Base 7 — Upper bound on s
There is no (70, 92, large)-net in base 7, because
- 20 times m-reduction [i] would yield (70, 72, large)-net in base 7, but