Best Known (48, 60, s)-Nets in Base 7
(48, 60, 2818)-Net over F7 — Constructive and digital
Digital (48, 60, 2818)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 16)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 8)-net over F7, using
- net from sequence [i] based on digital (0, 7)-sequence over F7, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using
- the rational function field F7(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 7)-sequence over F7, using
- digital (0, 6, 8)-net over F7, using
- net from sequence [i] based on digital (0, 7)-sequence over F7 (see above)
- digital (0, 3, 8)-net over F7, using
- (u, u+v)-construction [i] based on
- 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 (3, 9, 16)-net over F7, using
(48, 60, 33309)-Net over F7 — Digital
Digital (48, 60, 33309)-net over F7, using
(48, 60, large)-Net in Base 7 — Upper bound on s
There is no (48, 60, large)-net in base 7, because
- 10 times m-reduction [i] would yield (48, 50, large)-net in base 7, but