Best Known (83, 83+18, s)-Nets in Base 8
(83, 83+18, 29141)-Net over F8 — Constructive and digital
Digital (83, 101, 29141)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 14)-net over F8, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- digital (73, 91, 29127)-net over F8, using
- net defined by OOA [i] based on linear OOA(891, 29127, F8, 18, 18) (dual of [(29127, 18), 524195, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(891, 262143, F8, 18) (dual of [262143, 262052, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(891, 262144, F8, 18) (dual of [262144, 262053, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(891, 262144, F8, 18) (dual of [262144, 262053, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(891, 262143, F8, 18) (dual of [262143, 262052, 19]-code), using
- net defined by OOA [i] based on linear OOA(891, 29127, F8, 18, 18) (dual of [(29127, 18), 524195, 19]-NRT-code), using
- digital (1, 10, 14)-net over F8, using
(83, 83+18, 262190)-Net over F8 — Digital
Digital (83, 101, 262190)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8101, 262190, F8, 18) (dual of [262190, 262089, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- linear OA(891, 262144, F8, 18) (dual of [262144, 262053, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(855, 262144, F8, 11) (dual of [262144, 262089, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(17) ⊂ Ce(10) [i] based on
(83, 83+18, large)-Net in Base 8 — Upper bound on s
There is no (83, 101, large)-net in base 8, because
- 16 times m-reduction [i] would yield (83, 85, large)-net in base 8, but