Best Known (86, 100, s)-Nets in Base 4
(86, 100, 37460)-Net over F4 — Constructive and digital
Digital (86, 100, 37460)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 10)-net over F4, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 2 and N(F) ≥ 10, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- digital (77, 91, 37450)-net over F4, using
- net defined by OOA [i] based on linear OOA(491, 37450, F4, 14, 14) (dual of [(37450, 14), 524209, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(491, 262150, F4, 14) (dual of [262150, 262059, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(491, 262153, F4, 14) (dual of [262153, 262062, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(491, 262144, F4, 14) (dual of [262144, 262053, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(40, 9, F4, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(491, 262153, F4, 14) (dual of [262153, 262062, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(491, 262150, F4, 14) (dual of [262150, 262059, 15]-code), using
- net defined by OOA [i] based on linear OOA(491, 37450, F4, 14, 14) (dual of [(37450, 14), 524209, 15]-NRT-code), using
- digital (2, 9, 10)-net over F4, using
(86, 100, 163385)-Net over F4 — Digital
Digital (86, 100, 163385)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4100, 163385, F4, 14) (dual of [163385, 163285, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4100, 262154, F4, 14) (dual of [262154, 262054, 15]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(44, 5, F4, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,4)), using
- dual of repetition code with length 5 [i]
- linear OA(45, 5, F4, 5) (dual of [5, 0, 6]-code or 5-arc in PG(4,4)), using
- linear OA(491, 262144, F4, 14) (dual of [262144, 262053, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(44, 5, F4, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,4)), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4100, 262154, F4, 14) (dual of [262154, 262054, 15]-code), using
(86, 100, large)-Net in Base 4 — Upper bound on s
There is no (86, 100, large)-net in base 4, because
- 12 times m-reduction [i] would yield (86, 88, large)-net in base 4, but