Best Known (30−6, 30, s)-Nets in Base 7
(30−6, 30, 5654)-Net over F7 — Constructive and digital
Digital (24, 30, 5654)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 50)-net over F7, using
- net defined by OOA [i] based on linear OOA(74, 50, F7, 3, 3) (dual of [(50, 3), 146, 4]-NRT-code), using
- digital (20, 26, 5604)-net over F7, using
- net defined by OOA [i] based on linear OOA(726, 5604, F7, 6, 6) (dual of [(5604, 6), 33598, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(726, 16812, F7, 6) (dual of [16812, 16786, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(726, 16807, F7, 6) (dual of [16807, 16781, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(721, 16807, F7, 5) (dual of [16807, 16786, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(726, 16812, F7, 6) (dual of [16812, 16786, 7]-code), using
- net defined by OOA [i] based on linear OOA(726, 5604, F7, 6, 6) (dual of [(5604, 6), 33598, 7]-NRT-code), using
- digital (1, 4, 50)-net over F7, using
(30−6, 30, 51085)-Net over F7 — Digital
Digital (24, 30, 51085)-net over F7, using
(30−6, 30, large)-Net in Base 7 — Upper bound on s
There is no (24, 30, large)-net in base 7, because
- 4 times m-reduction [i] would yield (24, 26, large)-net in base 7, but