MinT - Best Known (108−91, 108, s)-Nets in Base 25

Best Known (108−91, 108, s)-Nets in Base 25

(108−91, 108, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 108, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 108, 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]

(108−91, 108, 150)-Net over F₂₅ — Digital

Digital (17, 108, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 108, 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]

(108−91, 108, 1524)-Net in Base 25 — Upper bound on s

There is no (17, 108, 1525)-net in base 25, because

1 times m-reduction [i] would yield (17, 107, 1525)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 381414 319496 296470 277224 184793 769100 692169 809219 081407 164376 711199 858503 549882 604880 947514 558188 608543 787850 424481 902620 483303 758230 333506 524547 223065 > 25¹⁰⁷ [i]