Best Known (95, 95+16, s)-Nets in Base 8
(95, 95+16, 262172)-Net over F8 — Constructive and digital
Digital (95, 111, 262172)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 13, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (82, 98, 262144)-net over F8, using
- net defined by OOA [i] based on linear OOA(898, 262144, F8, 16, 16) (dual of [(262144, 16), 4194206, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(898, 2097152, F8, 16) (dual of [2097152, 2097054, 17]-code), using
- 1 times truncation [i] based on linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using
- OA 8-folding and stacking [i] based on linear OA(898, 2097152, F8, 16) (dual of [2097152, 2097054, 17]-code), using
- net defined by OOA [i] based on linear OOA(898, 262144, F8, 16, 16) (dual of [(262144, 16), 4194206, 17]-NRT-code), using
- digital (5, 13, 28)-net over F8, using
(95, 95+16, 524289)-Net in Base 8 — Constructive
(95, 111, 524289)-net in base 8, using
- 81 times duplication [i] based on (94, 110, 524289)-net in base 8, using
- net defined by OOA [i] based on OOA(8110, 524289, S8, 16, 16), using
- OA 8-folding and stacking [i] based on OA(8110, 4194312, S8, 16), using
- discarding factors based on OA(8110, 4194318, S8, 16), using
- trace code [i] based on OA(6455, 2097159, S64, 16), using
- discarding parts of the base [i] based on linear OA(12847, 2097159, F128, 16) (dual of [2097159, 2097112, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding parts of the base [i] based on linear OA(12847, 2097159, F128, 16) (dual of [2097159, 2097112, 17]-code), using
- trace code [i] based on OA(6455, 2097159, S64, 16), using
- discarding factors based on OA(8110, 4194318, S8, 16), using
- OA 8-folding and stacking [i] based on OA(8110, 4194312, S8, 16), using
- net defined by OOA [i] based on OOA(8110, 524289, S8, 16, 16), using
(95, 95+16, 4421150)-Net over F8 — Digital
Digital (95, 111, 4421150)-net over F8, using
(95, 95+16, large)-Net in Base 8 — Upper bound on s
There is no (95, 111, large)-net in base 8, because
- 14 times m-reduction [i] would yield (95, 97, large)-net in base 8, but