MinT - Best Known (78−61, 78, s)-Nets in Base 25

Best Known (78−61, 78, s)-Nets in Base 25

(78−61, 78, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 78, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 78, 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]

(78−61, 78, 150)-Net over F₂₅ — Digital

Digital (17, 78, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 78, 150)-net over F₂₅, using
- net from sequence [i] based on digital (16, 149)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 16 and N(F) ≥ 150, using
    - an algebraic function field by Teo [i]

(78−61, 78, 1927)-Net in Base 25 — Upper bound on s

There is no (17, 78, 1928)-net in base 25, because

1 times m-reduction [i] would yield (17, 77, 1928)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 438223 253038 518246 068213 732072 595692 097452 456429 466225 395914 104419 170872 469311 122247 634467 358465 063339 622785 > 25⁷⁷ [i]