MinT - Best Known (97−74, 97, s)-Nets in Base 5

Best Known (97−74, 97, s)-Nets in Base 5

(97−74, 97, 51)-Net over F₅ — Constructive and digital

Digital (23, 97, 51)-net over F₅, using

t-expansion [i] based on digital (22, 97, 51)-net over F₅, using
- net from sequence [i] based on digital (22, 50)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
    - an explicitly constructive algebraic function field [i]

(97−74, 97, 55)-Net over F₅ — Digital

Digital (23, 97, 55)-net over F₅, using

net from sequence [i] based on digital (23, 54)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(97−74, 97, 135)-Net in Base 5 — Upper bound on s

There is no (23, 97, 136)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁹⁷, 136, S₅, 74), but
- the linear programming bound shows that MÂ â‰¥ 2405 164623 906243 095251 359659 995588 513786 389674 973546 898262 798110 490479 075451 730750 501155 853271 484375 / 36 631820 742075 818086 879608 746553 > 5⁹⁷ [i]