Best Known (68, 129, s)-Nets in Base 9
(68, 129, 232)-Net over F9 — Constructive and digital
Digital (68, 129, 232)-net over F9, using
- 3 times m-reduction [i] based on digital (68, 132, 232)-net over F9, using
- trace code for nets [i] based on digital (2, 66, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 66, 116)-net over F81, using
(68, 129, 310)-Net over F9 — Digital
Digital (68, 129, 310)-net over F9, using
(68, 129, 17729)-Net in Base 9 — Upper bound on s
There is no (68, 129, 17730)-net in base 9, because
- 1 times m-reduction [i] would yield (68, 128, 17730)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 139 219984 940956 715417 520934 772260 898533 064956 854618 576594 214476 249245 943063 358859 055639 964947 068517 506463 252192 722095 799329 > 9128 [i]