MinT - Best Known (87−63, 87, s)-Nets in Base 25

Best Known (87−63, 87, s)-Nets in Base 25

(87−63, 87, 148)-Net over F₂₅ — Constructive and digital

Digital (24, 87, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 87, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(87−63, 87, 184)-Net over F₂₅ — Digital

Digital (24, 87, 184)-net over F₂₅, using

net from sequence [i] based on digital (24, 183)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 24 and N(F) ≥ 184, using
  - an algebraic function field by Teo [i]

(87−63, 87, 3891)-Net in Base 25 — Upper bound on s

There is no (24, 87, 3892)-net in base 25, because

1 times m-reduction [i] would yield (24, 86, 3892)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1 671358 801315 829897 923434 122647 669417 421804 010030 955450 467470 448839 179693 068762 592432 884760 624092 950545 113325 465180 154785 > 25⁸⁶ [i]