Best Known (119, 119+25, s)-Nets in Base 8
(119, 119+25, 21873)-Net over F8 — Constructive and digital
Digital (119, 144, 21873)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 17, 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 (102, 127, 21845)-net over F8, using
- net defined by OOA [i] based on linear OOA(8127, 21845, F8, 25, 25) (dual of [(21845, 25), 545998, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8127, 262141, F8, 25) (dual of [262141, 262014, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8127, 262141, F8, 25) (dual of [262141, 262014, 26]-code), using
- net defined by OOA [i] based on linear OOA(8127, 21845, F8, 25, 25) (dual of [(21845, 25), 545998, 26]-NRT-code), using
- digital (5, 17, 28)-net over F8, using
(119, 119+25, 367129)-Net over F8 — Digital
Digital (119, 144, 367129)-net over F8, using
(119, 119+25, large)-Net in Base 8 — Upper bound on s
There is no (119, 144, large)-net in base 8, because
- 23 times m-reduction [i] would yield (119, 121, large)-net in base 8, but