Best Known (46, 58, s)-Nets in Base 7
(46, 58, 2815)-Net over F7 — Constructive and digital
Digital (46, 58, 2815)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 13)-net over F7, using
- 6 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (39, 51, 2802)-net over F7, using
- net defined by OOA [i] based on linear OOA(751, 2802, F7, 12, 12) (dual of [(2802, 12), 33573, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(751, 16812, F7, 12) (dual of [16812, 16761, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(751, 16807, F7, 12) (dual of [16807, 16756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- OA 6-folding and stacking [i] based on linear OA(751, 16812, F7, 12) (dual of [16812, 16761, 13]-code), using
- net defined by OOA [i] based on linear OOA(751, 2802, F7, 12, 12) (dual of [(2802, 12), 33573, 13]-NRT-code), using
- digital (1, 7, 13)-net over F7, using
(46, 58, 23385)-Net over F7 — Digital
Digital (46, 58, 23385)-net over F7, using
(46, 58, large)-Net in Base 7 — Upper bound on s
There is no (46, 58, large)-net in base 7, because
- 10 times m-reduction [i] would yield (46, 48, large)-net in base 7, but