Best Known (101−29, 101, s)-Nets in Base 9
(101−29, 101, 740)-Net over F9 — Constructive and digital
Digital (72, 101, 740)-net over F9, using
- 11 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
(101−29, 101, 4657)-Net over F9 — Digital
Digital (72, 101, 4657)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9101, 4657, F9, 29) (dual of [4657, 4556, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(9101, 6561, F9, 29) (dual of [6561, 6460, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(9101, 6561, F9, 29) (dual of [6561, 6460, 30]-code), using
(101−29, 101, 4947490)-Net in Base 9 — Upper bound on s
There is no (72, 101, 4947491)-net in base 9, because
- 1 times m-reduction [i] would yield (72, 100, 4947491)-net in base 9, but
- 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]