Best Known (89, 108, s)-Nets in Base 8
(89, 108, 29144)-Net over F8 — Constructive and digital
Digital (89, 108, 29144)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 17)-net over F8, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- digital (78, 97, 29127)-net over F8, using
- net defined by OOA [i] based on linear OOA(897, 29127, F8, 19, 19) (dual of [(29127, 19), 553316, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(897, 262144, F8, 19) (dual of [262144, 262047, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(897, 262144, F8, 19) (dual of [262144, 262047, 20]-code), using
- net defined by OOA [i] based on linear OOA(897, 29127, F8, 19, 19) (dual of [(29127, 19), 553316, 20]-NRT-code), using
- digital (2, 11, 17)-net over F8, using
(89, 108, 282869)-Net over F8 — Digital
Digital (89, 108, 282869)-net over F8, using
(89, 108, large)-Net in Base 8 — Upper bound on s
There is no (89, 108, large)-net in base 8, because
- 17 times m-reduction [i] would yield (89, 91, large)-net in base 8, but