Best Known (99, 99+38, s)-Nets in Base 9
(99, 99+38, 780)-Net over F9 — Constructive and digital
Digital (99, 137, 780)-net over F9, using
- t-expansion [i] based on digital (98, 137, 780)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 27, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- digital (71, 110, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 55, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 55, 370)-net over F81, using
- digital (8, 27, 40)-net over F9, using
- (u, u+v)-construction [i] based on
(99, 99+38, 6577)-Net over F9 — Digital
Digital (99, 137, 6577)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9137, 6577, F9, 38) (dual of [6577, 6440, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
- linear OA(9133, 6561, F9, 38) (dual of [6561, 6428, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(9121, 6561, F9, 34) (dual of [6561, 6440, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(94, 16, F9, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,9)), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
(99, 99+38, 7528623)-Net in Base 9 — Upper bound on s
There is no (99, 137, 7528624)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 53854 766564 979416 208604 166642 198961 133040 363841 398524 212685 622470 941717 058639 634161 174109 199440 118696 983773 506441 521902 713398 008449 > 9137 [i]