Best Known (19, 80, s)-Nets in Base 5
(19, 80, 43)-Net over F5 — Constructive and digital
Digital (19, 80, 43)-net over F5, using
- t-expansion [i] based on digital (18, 80, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
(19, 80, 45)-Net over F5 — Digital
Digital (19, 80, 45)-net over F5, using
- net from sequence [i] based on digital (19, 44)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 19 and N(F) ≥ 45, using
(19, 80, 126)-Net in Base 5 — Upper bound on s
There is no (19, 80, 127)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(580, 127, S5, 61), but
- the linear programming bound shows that M ≥ 3534 272221 730880 547258 511745 524357 514879 487167 609946 192606 669762 406320 395189 789074 219532 949427 957646 548748 016357 421875 / 40 493098 117659 814739 055947 504367 858428 910429 601519 845321 465114 > 580 [i]