Best Known (102−15, 102, s)-Nets in Base 8
(102−15, 102, 299618)-Net over F8 — Constructive and digital
Digital (87, 102, 299618)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- digital (77, 92, 299594)-net over F8, using
- net defined by OOA [i] based on linear OOA(892, 299594, F8, 15, 15) (dual of [(299594, 15), 4493818, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(892, 2097159, F8, 15) (dual of [2097159, 2097067, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(892, 2097152, F8, 15) (dual of [2097152, 2097060, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(80, 7, F8, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(892, 2097159, F8, 15) (dual of [2097159, 2097067, 16]-code), using
- net defined by OOA [i] based on linear OOA(892, 299594, F8, 15, 15) (dual of [(299594, 15), 4493818, 16]-NRT-code), using
- digital (3, 10, 24)-net over F8, using
(102−15, 102, 599187)-Net in Base 8 — Constructive
(87, 102, 599187)-net in base 8, using
- net defined by OOA [i] based on OOA(8102, 599187, S8, 15, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(8102, 4194310, S8, 15), using
- trace code [i] based on OA(6451, 2097155, S64, 15), using
- discarding parts of the base [i] based on linear OA(12843, 2097155, F128, 15) (dual of [2097155, 2097112, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- discarding parts of the base [i] based on linear OA(12843, 2097155, F128, 15) (dual of [2097155, 2097112, 16]-code), using
- trace code [i] based on OA(6451, 2097155, S64, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(8102, 4194310, S8, 15), using
(102−15, 102, 3281076)-Net over F8 — Digital
Digital (87, 102, 3281076)-net over F8, using
(102−15, 102, large)-Net in Base 8 — Upper bound on s
There is no (87, 102, large)-net in base 8, because
- 13 times m-reduction [i] would yield (87, 89, large)-net in base 8, but