Best Known (135−27, 135, s)-Nets in Base 9
(135−27, 135, 4562)-Net over F9 — Constructive and digital
Digital (108, 135, 4562)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 15, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (93, 120, 4542)-net over F9, using
- net defined by OOA [i] based on linear OOA(9120, 4542, F9, 27, 27) (dual of [(4542, 27), 122514, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9120, 59047, F9, 27) (dual of [59047, 58927, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9120, 59048, F9, 27) (dual of [59048, 58928, 28]-code), using
- 1 times truncation [i] based on linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 1 times truncation [i] based on linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9120, 59048, F9, 27) (dual of [59048, 58928, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9120, 59047, F9, 27) (dual of [59047, 58927, 28]-code), using
- net defined by OOA [i] based on linear OOA(9120, 4542, F9, 27, 27) (dual of [(4542, 27), 122514, 28]-NRT-code), using
- digital (2, 15, 20)-net over F9, using
(135−27, 135, 118842)-Net over F9 — Digital
Digital (108, 135, 118842)-net over F9, using
(135−27, 135, large)-Net in Base 9 — Upper bound on s
There is no (108, 135, large)-net in base 9, because
- 25 times m-reduction [i] would yield (108, 110, large)-net in base 9, but