Best Known (64−48, 64, s)-Nets in Base 5
(64−48, 64, 37)-Net over F5 — Constructive and digital
Digital (16, 64, 37)-net over F5, using
- net from sequence [i] based on digital (16, 36)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 5 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(64−48, 64, 40)-Net over F5 — Digital
Digital (16, 64, 40)-net over F5, using
- net from sequence [i] based on digital (16, 39)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 16 and N(F) ≥ 40, using
(64−48, 64, 137)-Net in Base 5 — Upper bound on s
There is no (16, 64, 138)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(564, 138, S5, 48), but
- the linear programming bound shows that M ≥ 618 188381 460855 172675 468308 247294 560317 257333 010740 671089 381266 901996 604847 127745 640952 510318 810727 549500 502077 158082 867676 892294 583854 036813 136869 109398 247684 305084 343952 041306 937677 054130 227156 228285 893824 203611 757184 262387 454509 735107 421875 / 1 067016 340107 492572 230424 186915 788238 736393 798602 531197 750956 411280 536009 313715 193698 075426 896087 041430 213225 757018 472796 210899 646763 502126 479063 983701 081512 488985 765185 148179 060056 483237 448611 149267 > 564 [i]