Best Known (81, 105, s)-Nets in Base 7
(81, 105, 1402)-Net over F7 — Constructive and digital
Digital (81, 105, 1402)-net over F7, using
- net defined by OOA [i] based on linear OOA(7105, 1402, F7, 24, 24) (dual of [(1402, 24), 33543, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(7105, 16824, F7, 24) (dual of [16824, 16719, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(7105, 16826, F7, 24) (dual of [16826, 16721, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- linear OA(7101, 16807, F7, 24) (dual of [16807, 16706, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(74, 19, F7, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,7)), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(7105, 16826, F7, 24) (dual of [16826, 16721, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(7105, 16824, F7, 24) (dual of [16824, 16719, 25]-code), using
(81, 105, 14904)-Net over F7 — Digital
Digital (81, 105, 14904)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(7105, 14904, F7, 24) (dual of [14904, 14799, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(7105, 16826, F7, 24) (dual of [16826, 16721, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- linear OA(7101, 16807, F7, 24) (dual of [16807, 16706, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(74, 19, F7, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,7)), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(7105, 16826, F7, 24) (dual of [16826, 16721, 25]-code), using
(81, 105, large)-Net in Base 7 — Upper bound on s
There is no (81, 105, large)-net in base 7, because
- 22 times m-reduction [i] would yield (81, 83, large)-net in base 7, but