Best Known (14, 14+41, s)-Nets in Base 5
(14, 14+41, 35)-Net over F5 — Constructive and digital
Digital (14, 55, 35)-net over F5, using
- net from sequence [i] based on digital (14, 34)-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 3 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]
(14, 14+41, 39)-Net over F5 — Digital
Digital (14, 55, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
(14, 14+41, 131)-Net in Base 5 — Upper bound on s
There is no (14, 55, 132)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(555, 132, S5, 41), but
- the linear programming bound shows that M ≥ 26 229549 012015 749664 509480 322141 685578 113295 187522 256579 852565 802733 072478 660550 435809 150517 538768 099257 140420 377254 486083 984375 / 92326 024696 659009 680757 535405 805246 427877 728103 389905 774710 516572 331042 057214 363816 301671 > 555 [i]