Best Known (62, 62+14, s)-Nets in Base 5
(62, 62+14, 2245)-Net over F5 — Constructive and digital
Digital (62, 76, 2245)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 12)-net over F5, using
- net from sequence [i] based on digital (2, 11)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 2 and N(F) ≥ 12, using
- net from sequence [i] based on digital (2, 11)-sequence over F5, using
- digital (53, 67, 2233)-net over F5, using
- net defined by OOA [i] based on linear OOA(567, 2233, F5, 14, 14) (dual of [(2233, 14), 31195, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(567, 15631, F5, 14) (dual of [15631, 15564, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(561, 15625, F5, 13) (dual of [15625, 15564, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(50, 6, F5, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- OA 7-folding and stacking [i] based on linear OA(567, 15631, F5, 14) (dual of [15631, 15564, 15]-code), using
- net defined by OOA [i] based on linear OOA(567, 2233, F5, 14, 14) (dual of [(2233, 14), 31195, 15]-NRT-code), using
- digital (2, 9, 12)-net over F5, using
(62, 62+14, 17290)-Net over F5 — Digital
Digital (62, 76, 17290)-net over F5, using
(62, 62+14, large)-Net in Base 5 — Upper bound on s
There is no (62, 76, large)-net in base 5, because
- 12 times m-reduction [i] would yield (62, 64, large)-net in base 5, but