Best Known (66−45, 66, s)-Nets in Base 4
(66−45, 66, 34)-Net over F4 — Constructive and digital
Digital (21, 66, 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
(66−45, 66, 44)-Net over F4 — Digital
Digital (21, 66, 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
(66−45, 66, 149)-Net in Base 4 — Upper bound on s
There is no (21, 66, 150)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(466, 150, S4, 45), but
- the linear programming bound shows that M ≥ 218 603248 395353 963143 573129 094845 574107 874696 792745 859935 933646 235876 315511 128217 770614 833515 398023 492482 446101 600214 474162 958366 887001 317163 943539 507200 000000 / 39636 522622 025040 367641 896273 764902 619875 534086 883796 962530 116095 725635 815042 105519 857817 694911 172894 869760 633227 396889 > 466 [i]