Best Known (83−72, 83, s)-Nets in Base 9
(83−72, 83, 40)-Net over F9 — Constructive and digital
Digital (11, 83, 40)-net over F9, using
- t-expansion [i] based on digital (8, 83, 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
(83−72, 83, 55)-Net over F9 — Digital
Digital (11, 83, 55)-net over F9, using
- net from sequence [i] based on digital (11, 54)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 11 and N(F) ≥ 55, using
(83−72, 83, 188)-Net over F9 — Upper bound on s (digital)
There is no digital (11, 83, 189)-net over F9, because
- extracting embedded orthogonal array [i] would yield linear OA(983, 189, F9, 72) (dual of [189, 106, 73]-code), but
- residual code [i] would yield OA(911, 116, S9, 8), but
- the linear programming bound shows that M ≥ 5 499012 279435 406875 / 174 903739 > 911 [i]
- residual code [i] would yield OA(911, 116, S9, 8), but
(83−72, 83, 224)-Net in Base 9 — Upper bound on s
There is no (11, 83, 225)-net in base 9, because
- 18 times m-reduction [i] would yield (11, 65, 225)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(965, 225, S9, 54), but
- the linear programming bound shows that M ≥ 1 407158 071957 405502 080634 170649 666681 351029 811313 477564 249946 509212 567552 061950 290997 535422 640957 000607 894786 170825 293062 081202 608589 929200 / 12919 598267 682231 631223 118900 223172 391171 482474 551992 207926 453044 062169 872017 > 965 [i]
- extracting embedded orthogonal array [i] would yield OA(965, 225, S9, 54), but