Best Known (138, 138+29, s)-Nets in Base 8
(138, 138+29, 18741)-Net over F8 — Constructive and digital
Digital (138, 167, 18741)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 16, 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 (122, 151, 18724)-net over F8, using
- net defined by OOA [i] based on linear OOA(8151, 18724, F8, 29, 29) (dual of [(18724, 29), 542845, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8151, 262137, F8, 29) (dual of [262137, 261986, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8151, 262144, F8, 29) (dual of [262144, 261993, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(8151, 262144, F8, 29) (dual of [262144, 261993, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8151, 262137, F8, 29) (dual of [262137, 261986, 30]-code), using
- net defined by OOA [i] based on linear OOA(8151, 18724, F8, 29, 29) (dual of [(18724, 29), 542845, 30]-NRT-code), using
- digital (2, 16, 17)-net over F8, using
(138, 138+29, 392834)-Net over F8 — Digital
Digital (138, 167, 392834)-net over F8, using
(138, 138+29, large)-Net in Base 8 — Upper bound on s
There is no (138, 167, large)-net in base 8, because
- 27 times m-reduction [i] would yield (138, 140, large)-net in base 8, but