Best Known (79, 96, s)-Nets in Base 8
(79, 96, 32792)-Net over F8 — Constructive and digital
Digital (79, 96, 32792)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 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 (68, 85, 32768)-net over F8, using
- net defined by OOA [i] based on linear OOA(885, 32768, F8, 17, 17) (dual of [(32768, 17), 556971, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
- net defined by OOA [i] based on linear OOA(885, 32768, F8, 17, 17) (dual of [(32768, 17), 556971, 18]-NRT-code), using
- digital (3, 11, 24)-net over F8, using
(79, 96, 262192)-Net over F8 — Digital
Digital (79, 96, 262192)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(896, 262192, F8, 17) (dual of [262192, 262096, 18]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(895, 262190, F8, 17) (dual of [262190, 262095, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- linear OA(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(849, 262144, F8, 10) (dual of [262144, 262095, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(810, 46, F8, 6) (dual of [46, 36, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- construction X applied to Ce(16) ⊂ Ce(9) [i] based on
- linear OA(895, 262191, F8, 16) (dual of [262191, 262096, 17]-code), using Gilbert–Varšamov bound and bm = 895 > Vbs−1(k−1) = 6903 072994 065942 986818 295914 172443 542469 706915 278935 609030 293435 749148 177587 399632 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 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
- linear OA(895, 262190, F8, 17) (dual of [262190, 262095, 18]-code), using
- construction X with Varšamov bound [i] based on
(79, 96, large)-Net in Base 8 — Upper bound on s
There is no (79, 96, large)-net in base 8, because
- 15 times m-reduction [i] would yield (79, 81, large)-net in base 8, but