Best Known (38, 38+79, s)-Nets in Base 9
(38, 38+79, 81)-Net over F9 — Constructive and digital
Digital (38, 117, 81)-net over F9, using
- t-expansion [i] based on digital (32, 117, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(38, 38+79, 128)-Net over F9 — Digital
Digital (38, 117, 128)-net over F9, using
- t-expansion [i] based on digital (33, 117, 128)-net over F9, using
- net from sequence [i] based on digital (33, 127)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 33 and N(F) ≥ 128, using
- net from sequence [i] based on digital (33, 127)-sequence over F9, using
(38, 38+79, 1302)-Net in Base 9 — Upper bound on s
There is no (38, 117, 1303)-net in base 9, because
- 1 times m-reduction [i] would yield (38, 116, 1303)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 500 834632 057675 979042 530489 699434 497523 514116 742211 224315 845350 707410 781793 378606 286488 578202 518684 214184 596745 > 9116 [i]