MinT - Best Known (80−41, 80, s)-Nets in Base 25

Best Known (80−41, 80, s)-Nets in Base 25

(80−41, 80, 230)-Net over F₂₅ — Constructive and digital

Digital (39, 80, 230)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (9, 29, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]
2. digital (10, 51, 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]

(80−41, 80, 419)-Net over F₂₅ — Digital

Digital (39, 80, 419)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−41, 80, 115058)-Net in Base 25 — Upper bound on s

There is no (39, 80, 115059)-net in base 25, because

1 times m-reduction [i] would yield (39, 79, 115059)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 273 710930 085859 632383 698213 778610 754286 083171 246108 171981 613305 240167 689452 188057 106193 200391 731096 565642 246305 > 25⁷⁹ [i]