Best Known (107−16, 107, s)-Nets in Base 9
(107−16, 107, 597882)-Net over F9 — Constructive and digital
Digital (91, 107, 597882)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 10)-net over F9, using
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 0 and N(F) ≥ 10, using
- the rational function field F9(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- digital (83, 99, 597872)-net over F9, using
- net defined by OOA [i] based on linear OOA(999, 597872, F9, 16, 16) (dual of [(597872, 16), 9565853, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(999, 4782976, F9, 16) (dual of [4782976, 4782877, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- OA 8-folding and stacking [i] based on linear OA(999, 4782976, F9, 16) (dual of [4782976, 4782877, 17]-code), using
- net defined by OOA [i] based on linear OOA(999, 597872, F9, 16, 16) (dual of [(597872, 16), 9565853, 17]-NRT-code), using
- digital (0, 8, 10)-net over F9, using
(107−16, 107, 5147628)-Net over F9 — Digital
Digital (91, 107, 5147628)-net over F9, using
(107−16, 107, large)-Net in Base 9 — Upper bound on s
There is no (91, 107, large)-net in base 9, because
- 14 times m-reduction [i] would yield (91, 93, large)-net in base 9, but