MinT - Best Known (102−56, 102, s)-Nets in Base 25

Best Known (102−56, 102, s)-Nets in Base 25

(102−56, 102, 288)-Net over F₂₅ — Constructive and digital

Digital (46, 102, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 102, 288)-net over F₂₅, using
- net from sequence [i] based on digital (41, 287)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288, using
    - a function field by GarcÃa and Quoos [i]

(102−56, 102, 338)-Net over F₂₅ — Digital

Digital (46, 102, 338)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−56, 102, 58234)-Net in Base 25 — Upper bound on s

There is no (46, 102, 58235)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 38903 637934 974813 472310 701090 139407 603562 775112 760446 094227 036385 543583 335071 590726 623608 513998 847575 592589 414969 962301 670527 338814 337745 820641 > 25¹⁰² [i]