MinT - Best Known (110−95, 110, s)-Nets in Base 25

Best Known (110−95, 110, s)-Nets in Base 25

(110−95, 110, 126)-Net over F₂₅ — Constructive and digital

Digital (15, 110, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 110, 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]

(110−95, 110, 140)-Net over F₂₅ — Digital

Digital (15, 110, 140)-net over F₂₅, using

net from sequence [i] based on digital (15, 139)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 15 and N(F) ≥ 140, using
  - an algebraic function field by Teo [i]

(110−95, 110, 1311)-Net in Base 25 — Upper bound on s

There is no (15, 110, 1312)-net in base 25, because

1 times m-reduction [i] would yield (15, 109, 1312)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 241 668843 157763 426606 658434 053116 931013 870024 291036 134705 523194 499567 288551 109942 883658 730020 017999 477350 626634 998799 072459 015709 116235 377832 302087 764225 > 25¹⁰⁹ [i]