Best Known (65−44, 65, s)-Nets in Base 4
(65−44, 65, 34)-Net over F4 — Constructive and digital
Digital (21, 65, 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
(65−44, 65, 44)-Net over F4 — Digital
Digital (21, 65, 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
(65−44, 65, 155)-Net in Base 4 — Upper bound on s
There is no (21, 65, 156)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(465, 156, S4, 44), but
- the linear programming bound shows that M ≥ 5305 672794 944537 381320 515598 514645 629008 946704 424695 546266 632663 854579 036277 493526 466626 448910 185539 633024 632652 385646 851129 344000 / 3 530621 465654 281569 250779 664225 038700 823798 252333 134165 234221 216150 895884 348866 248497 833837 > 465 [i]