MinT - Best Known (61, 61+43, s)-Nets in Base 25

Best Known (61, 61+43, s)-Nets in Base 25

(61, 61+43, 330)-Net over F₂₅ — Constructive and digital

Digital (61, 104, 330)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (10, 31, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]
2. digital (30, 73, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(61, 61+43, 2012)-Net over F₂₅ — Digital

Digital (61, 104, 2012)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+43, 2599216)-Net in Base 25 — Upper bound on s

There is no (61, 104, 2599217)-net in base 25, because

1 times m-reduction [i] would yield (61, 103, 2599217)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 972352 282137 766149 098525 938696 484741 953521 806751 631336 406888 952462 134305 044966 426701 788397 717680 729828 384796 668114 394160 889315 773113 126792 483065 > 25¹⁰³ [i]