MinT - Best Known (38, 38+59, s)-Nets in Base 25

Best Known (38, 38+59, s)-Nets in Base 25

(38, 38+59, 208)-Net over F₂₅ — Constructive and digital

Digital (38, 97, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 97, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(38, 38+59, 20618)-Net in Base 25 — Upper bound on s

There is no (38, 97, 20619)-net in base 25, because

1 times m-reduction [i] would yield (38, 96, 20619)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 159 452801 699427 792322 999579 422103 611107 241229 058443 078116 107291 718386 121457 575170 375548 511434 611339 727892 122562 664084 580381 915017 086185 > 25⁹⁶ [i]