Best Known (108−23, 108, s)-Nets in Base 7
(108−23, 108, 1541)-Net over F7 — Constructive and digital
Digital (85, 108, 1541)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 13)-net over F7, using
- 1 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (73, 96, 1528)-net over F7, using
- net defined by OOA [i] based on linear OOA(796, 1528, F7, 23, 23) (dual of [(1528, 23), 35048, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(796, 16809, F7, 23) (dual of [16809, 16713, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(796, 16812, F7, 23) (dual of [16812, 16716, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(796, 16807, F7, 23) (dual of [16807, 16711, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(70, 5, F7, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(796, 16812, F7, 23) (dual of [16812, 16716, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(796, 16809, F7, 23) (dual of [16809, 16713, 24]-code), using
- net defined by OOA [i] based on linear OOA(796, 1528, F7, 23, 23) (dual of [(1528, 23), 35048, 24]-NRT-code), using
- digital (1, 12, 13)-net over F7, using
(108−23, 108, 21261)-Net over F7 — Digital
Digital (85, 108, 21261)-net over F7, using
(108−23, 108, large)-Net in Base 7 — Upper bound on s
There is no (85, 108, large)-net in base 7, because
- 21 times m-reduction [i] would yield (85, 87, large)-net in base 7, but