Best Known (72, 100, s)-Nets in Base 9
(72, 100, 740)-Net over F9 — Constructive and digital
Digital (72, 100, 740)-net over F9, using
- 12 times m-reduction [i] based on digital (72, 112, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 56, 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, 56, 370)-net over F81, using
(72, 100, 5656)-Net over F9 — Digital
Digital (72, 100, 5656)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9100, 5656, F9, 28) (dual of [5656, 5556, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9100, 6572, F9, 28) (dual of [6572, 6472, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(999, 6571, F9, 28) (dual of [6571, 6472, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(997, 6561, F9, 28) (dual of [6561, 6464, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(989, 6561, F9, 25) (dual of [6561, 6472, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(999, 6571, F9, 28) (dual of [6571, 6472, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9100, 6572, F9, 28) (dual of [6572, 6472, 29]-code), using
(72, 100, 4947490)-Net in Base 9 — Upper bound on s
There is no (72, 100, 4947491)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 265614 502915 136427 349357 207745 173068 547042 534650 251041 923383 524591 972694 307201 149250 453961 690065 > 9100 [i]