MinT - Best Known (6, 6+10, s)-Nets in Base 25

Best Known (6, 6+10, s)-Nets in Base 25

(6, 6+10, 66)-Net over F₂₅ — Constructive and digital

Digital (6, 16, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 16, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(6, 6+10, 67)-Net over F₂₅ — Digital

Digital (6, 16, 67)-net over F₂₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(25¹⁶, 67, F₂₅, 2, 10) (dual of [(67, 2), 118, 11]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25¹⁴, 66, F₂₅, 2, 10) (dual of [(66, 2), 118, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,121P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(6, 6+10, 3226)-Net in Base 25 — Upper bound on s

There is no (6, 16, 3227)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 23299 949873 870473 902505 > 25¹⁶ [i]