Best Known (22, 69, s)-Nets in Base 4
(22, 69, 34)-Net over F4 — Constructive and digital
Digital (22, 69, 34)-net over F4, using
- t-expansion [i] based on digital (21, 69, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
(22, 69, 44)-Net over F4 — Digital
Digital (22, 69, 44)-net over F4, using
- t-expansion [i] based on digital (21, 69, 44)-net over F4, using
- net from sequence [i] based on digital (21, 43)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 44, using
- net from sequence [i] based on digital (21, 43)-sequence over F4, using
(22, 69, 159)-Net in Base 4 — Upper bound on s
There is no (22, 69, 160)-net in base 4, because
- 1 times m-reduction [i] would yield (22, 68, 160)-net in base 4, but
- extracting embedded orthogonal array [i] would yield OA(468, 160, S4, 46), but
- the linear programming bound shows that M ≥ 10178 629433 929836 486543 068800 140163 269042 043780 022134 664338 507769 510819 622533 364638 543087 235674 689592 586232 641534 482804 572425 994198 736437 248000 / 113203 572801 045878 145860 058818 437218 882917 411800 440768 742206 357256 206420 022337 868833 760142 804084 942919 > 468 [i]
- extracting embedded orthogonal array [i] would yield OA(468, 160, S4, 46), but