MinT - Best Known (63−46, 63, s)-Nets in Base 5

Best Known (63−46, 63, s)-Nets in Base 5

(63−46, 63, 42)-Net over F₅ — Constructive and digital

Digital (17, 63, 42)-net over F₅, using

net from sequence [i] based on digital (17, 41)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 17 and N(F) ≥ 42, using
  - an explicitly constructive algebraic function field [i]

(63−46, 63, 163)-Net in Base 5 — Upper bound on s

There is no (17, 63, 164)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁶³, 164, S₅, 46), but
- the linear programming bound shows that MÂ â‰¥ 264 425865 237037 699557 911700 773256 300918 932644 013509 938844 284267 344755 200847 814758 991007 531427 963687 914434 398606 999820 913188 159465 789794 921875 / 2 325486 845508 858489 325940 763770 950467 937497 727285 731646 422111 274260 936155 889078 605086 915671 963203 > 5⁶³ [i]