MinT - Best Known (60, 110, s)-Nets in Base 25

Best Known (60, 110, s)-Nets in Base 25

(60, 110, 326)-Net over F₂₅ — Constructive and digital

Digital (60, 110, 326)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (10, 35, 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 (25, 75, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(60, 110, 1119)-Net over F₂₅ — Digital

Digital (60, 110, 1119)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 110, 600262)-Net in Base 25 — Upper bound on s

There is no (60, 110, 600263)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 5934 861852 262497 820566 675171 889849 104328 818394 565352 488244 023169 429104 594277 011725 594452 399684 024780 852584 296446 551435 073433 937546 754801 520504 139274 626665 > 25¹¹⁰ [i]