Best Known (119, 119+30, s)-Nets in Base 9
(119, 119+30, 3964)-Net over F9 — Constructive and digital
Digital (119, 149, 3964)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- digital (101, 131, 3936)-net over F9, using
- net defined by OOA [i] based on linear OOA(9131, 3936, F9, 30, 30) (dual of [(3936, 30), 117949, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(9131, 59040, F9, 30) (dual of [59040, 58909, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(9131, 59049, F9, 30) (dual of [59049, 58918, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(9131, 59049, F9, 30) (dual of [59049, 58918, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(9131, 59040, F9, 30) (dual of [59040, 58909, 31]-code), using
- net defined by OOA [i] based on linear OOA(9131, 3936, F9, 30, 30) (dual of [(3936, 30), 117949, 31]-NRT-code), using
- digital (3, 18, 28)-net over F9, using
(119, 119+30, 116659)-Net over F9 — Digital
Digital (119, 149, 116659)-net over F9, using
(119, 119+30, large)-Net in Base 9 — Upper bound on s
There is no (119, 149, large)-net in base 9, because
- 28 times m-reduction [i] would yield (119, 121, large)-net in base 9, but