Best Known (14, 14+35, s)-Nets in Base 4
(14, 14+35, 30)-Net over F4 — Constructive and digital
Digital (14, 49, 30)-net over F4, using
- t-expansion [i] based on digital (13, 49, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 from the 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) = 13 and N(F) ≥ 30, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
(14, 14+35, 33)-Net over F4 — Digital
Digital (14, 49, 33)-net over F4, using
- t-expansion [i] based on digital (13, 49, 33)-net over F4, using
- net from sequence [i] based on digital (13, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 33, using
- net from sequence [i] based on digital (13, 32)-sequence over F4, using
(14, 14+35, 94)-Net in Base 4 — Upper bound on s
There is no (14, 49, 95)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(449, 95, S4, 35), but
- the linear programming bound shows that M ≥ 41192 474812 375713 789000 699456 975821 961965 744513 198426 307979 395590 830886 737800 969827 312304 732817 560215 797035 362301 689741 847926 242075 544191 768132 126714 956760 481792 / 121742 667562 520763 956640 695430 713637 859834 747719 323855 290261 057074 960416 613540 339354 221353 298210 726466 255682 521963 771033 504571 810965 > 449 [i]