Best Known (138−28, 138, s)-Nets in Base 9
(138−28, 138, 4245)-Net over F9 — Constructive and digital
Digital (110, 138, 4245)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 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 (93, 121, 4217)-net over F9, using
- net defined by OOA [i] based on linear OOA(9121, 4217, F9, 28, 28) (dual of [(4217, 28), 117955, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(9121, 59038, F9, 28) (dual of [59038, 58917, 29]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(9121, 59038, F9, 28) (dual of [59038, 58917, 29]-code), using
- net defined by OOA [i] based on linear OOA(9121, 4217, F9, 28, 28) (dual of [(4217, 28), 117955, 29]-NRT-code), using
- digital (3, 17, 28)-net over F9, using
(138−28, 138, 102947)-Net over F9 — Digital
Digital (110, 138, 102947)-net over F9, using
(138−28, 138, large)-Net in Base 9 — Upper bound on s
There is no (110, 138, large)-net in base 9, because
- 26 times m-reduction [i] would yield (110, 112, large)-net in base 9, but